<PAGE>
 
                                                                EXHIBIT 10.29

                                AMENDMENT TO

                           STOCK OPTION AGREEMENTS



   This Amendment to Stock Option Agreements is entered into effective as of
April 30, 1997, by and between Access Health, Inc. (the "Company"), and Kenneth
B. Plumlee ("Optionee").

                                  RECITALS
                                  --------

   WHEREAS, Optionee has heretofore been granted four different options by the
Company to purchase specified numbers of shares of its common stock (the
"Options"), said Options being evinced by four different Stock Option
Agreements, and the Parties desire to amend certain of the Stock Option
Agreements as hereinafter stated.

   WHEREAS, Optionee has refrained from exercising any of the Options in such a
manner as would have provided to him certain tax benefits to the detriment of
the Company.

   NOW, THEREFORE, in consideration of the foregoing and the mutual promises
made herein, the Company and Optionee (collectively referred to as the
"Parties") hereby agree as follows:

   1.  Options Held.  The Parties confirm that Optionee holds the following four
       ------------                                                             
       Options:

           An Option granted on January 29, 1993, to purchase 37,321
           shares of the Company's common stock at an exercise price
           of $4.167 per share (the "1993 Option");
       
           An Option granted on March 22, 1994, to purchase 37,321
           shares of the Company's common stock at an exercise price
           of $8.833 per share (the "1994 Option");
       
           An Option granted on May 23, 1995, to purchase 60,000
           shares of the Company's common stock at an exercise price
           of $10.420 per share (the "1995 Option"); and
       
           An Option granted on March 27, 1996, to purchase 112,500
           shares of the Company's common stock at an exercise price
           of $39.313 per share (the "1996 Option"), which option
           Employee has exchanged effective on the date hereof for a
           new option to purchase 112,500 shares of the Company's
           common stock at an exercise price of $14.395 per share
           (the closing price on May 1, 1997) which option shall
           become exercisable as to 10,227 shares at the end of each
           month beginning on May 31 with a final vesting of 10,230
           shares on the earlier of March 31, 1998, or the date of
           the 1998 annual meeting of stockholders (the "1997
           Option").

   2.  Current Status.  The Parties acknowledge and confirm to each other that
       --------------                                                         
all of the Options listed in Paragraph 1 above remain outstanding as of this
date, and that upon Optionee's exercise of any of the Options, the Options will
be treated as "non-qualified" Options under applicable tax laws and regulations.

   3.  1993 and 1994 Options.  The Parties acknowledge and confirm to each other
       ---------------------                                                    
that the 1993 Option and the 1994 Option are fully vested and all the shares
thereunder are subject to being purchased by Optionee at this time.

   4.  1995 Option.  The Parties acknowledge and confirm to each other that
       -----------                                                         
48,000 of the 60,000 shares in the 1995 Option are now vested and exercisable,
and the final 12,000 shares will become exercisable on May 23, 1997.
<PAGE>
 
   5.  Further Vesting.  Those portions of any of the Options not yet vested and
       ---------------                                                          
exercisable shall continue to vest and become exercisable for so long as, and
only for so long as, Optionee continues to serve as a director of the Company as
provided in Paragraph 4(c) of that certain Employment Agreement between Optionee
and the Company dated December 1, 1996, except as the Options may be accelerated
hereafter as provided in Paragraph 4(d) of that Employment Agreement.

   6.  Exercise Periods.  The Parties hereby agree that Paragraph 4(e) of that
       ----------------                                                       
certain Employment Agreement between Optionee and the Company dated December 1,
1996 relating to the extension of exercise periods is hereby deleted ab initio
and shall be null and void and of no force or effect as though it had never been
written.  Instead, the parties agree that the following shall be the exercise
periods for the Options.

       (a) 1993 and 1994 Options.  Subject to Paragraph 7 below, Optionee shall
           ---------------------                                               
have the right to exercise the 1993 and 1994 Options and to purchase any of the
shares covered thereby pursuant to the terms of those Options at any time from
now through the 90-day period following the date Optionee no longer serves on
the Company's Board of Directors.

       (b) 1995 Option (1).  Subject to Paragraph 7 below, Optionee shall have
           ---------------                                                    
the right to exercise the 1995 Option and to purchase any of the 12,000 shares
covered thereby, which were already vested as of the date hereof, pursuant to
the terms of that Option at any time from now through the 90-day period
following the date Optionee no longer serves on the Company's Board of
Directors.

       (c) 1995 Option (2).  Subject to Paragraph 7 below, Optionee shall have
           ---------------                                                    
the right to exercise the 1995 Option and to purchase any of the 36,000 shares
covered thereby, the vesting of which were accelerated pursuant to an Amendment
dated April 30, 1997 to that certain Employment Agreement between Optionee and
the Company dated December 1, 1996, pursuant to the terms of that Option at any
time from now through the 12-month period following the latter of (i) September
30, 1998 or (ii) the date Optionee no longer serves on the Company's Board of
Directors.

       (d) 1995 Option (3).  Subject to Paragraph 7 below, Optionee shall have
           ---------------                                                    
the right to exercise the 1995 Option and to purchase any of the 12,000 shares
covered thereby, which will become vested on May 23, 1997, pursuant to the terms
of that Option at any time from the date they become vested through the 90-day
period following the date Optionee no longer serves on the Company's Board of
Directors.

       (e) 1997 Option.  Subject to Paragraph 7 below, Optionee shall have the
           -----------                                                        
right to exercise the 1997 Option and to purchase any of the shares covered
thereby pursuant to the terms of that Option at any time from the dates those
shares become vested through the 12-month period following the latter of (i)
September 30, 1998 or (ii) the date Optionee no longer serves on the Company's
Board of Directors.

   7.  Term/Expiration Date.  The Parties acknowledge and confirm to each other
       --------------------                                                    
that each of the Stock Option Agreements specifies a "Term/Expiration Date"
seven years following the date of grant of the Option specified in the
particular Stock Option Agreement, after which Term/Expiration Date, Optionee
will have no further right to exercise the Option covered by that Stock Option
Agreement.

   8.  No Other Changes.  Except as expressly amended hereby, the Agreement
       ----------------                                                    
shall remain in full force and effect.

   9.  No Representations.  Each of the Parties represents that it or he has had
       ------------------                                                       
the opportunity to consult with an attorney, and has carefully read and
understands the scope and effect of the provisions of this Amendment.  Neither
Party has relied upon any representations or statements made by the other Party
hereto not specifically set forth in this Amendment.

                                     -2-
<PAGE>
 
   10. No Oral Modification.  The Stock Option Agreements and this Amendment may
       --------------------                                                     
only be amended in writing signed by Optionee and an officer of the Company.

   11. Governing Law.  This Amendment shall be governed by the laws of the State
       -------------                                                            
of California, without reference to its choice of law principles.

   12. Counterparts.  This Amendment may be executed in counterparts, and each
       ------------                                                           
counterpart shall have the same force and effect as an original and shall
constitute an effective, binding agreement on the part of each of the
undersigned.

   IN WITNESS WHEREOF, the Parties have executed this Amendment to Stock Option
Agreements as of the date set forth above.

                    ACCESS HEALTH, INC.

                    by  /s/ Julie A. Brooks
                       ____________________________________________
                         Julie A. Brooks
                         Senior Vice-President and General Counsel

                      /s/ Kenneth B. Plumlee
                    ______________________________________________
                    KENNETH B. PLUMLEE

                                     -3-