Should you continue to be the disciplinarian in your family your relationship with your stepdaughter will suffer. This should be her father's role, as you suggest and not yours. One of the strongest predictor's for success in stepfamily development is the relationship between stepparent and stepchild. The second strongest predictor is a good couples' bond. Since the biological bond between parent and child predates the couples' relationship, the need to honor and respect the boundaries of this previous bond is essential prior to fully incorporating a stepparent as a major authority figure.
Any shortcuts precipitate problems later.
Oftentimes, because of cultural loading on mothers to be the primary caregivers, stepmothers are susceptible to being placed in this role precipitously. Do not take this role on. Love includes discipline. Your husband is failing to cope with parenthood. Perhaps the dynamic in his last marriage was to leave this part of the job to Mom and he is attempting to do the same here.