I am about to have my third child under the age of 4.  What car should I get that would fit my family of 5, 3 kids in car seats, a dog and the possibility of adding another child in a few years?

You should consider test driving and purchasing a minivan.  With three children under the age of five, all of which are going to need to be in car seats for the foresee able future, the built in features of a minivan are going to fit your current and short term needs.  They include, but are not limited to automatic side doors, automatic rear doors, front, backup, and in cabin cameras, in car vacuum, parking assist, cruise control, built-in sun shades, captain chairs with a removable middle seat and rear entertainment.  A minivan can easily sit 8 adults or children comfortably.  It is the perfect car for a family of five or more should your family grow.