And also, it is really important to determine if the private school is a FAFSA-only school or if it uses the CSS Profile, as many (although certainly not most) private schools do. If it is a profile school, then they will be looking at both sets of parents’ financials from year 1.
It is also important to find out if the private school will stack the merit money for local students on top of any need-based aid, or if it is in place of a portion of the need-based aid for those who require it. Policies differ for different schools and that could make a real difference in your planning.
Also each college has to post a net price calculator on their webpage. You can go there and enter in different financial scenarios to see how the numbers play out
Reiterating what I posted above that the best solution may be for your step-daughter to find a major at the state school that she can embrace – or at the very least live with. It seems that would solve a lot of the problems, and since kids change their majors often once in school, maybe she can be induced to change her preference now?