First of congratulations to your daughter. She must have worked incredibly hard to get those grades.
While I am not from those institutes, it would be a shame to lose the opportunity you do have.
For most institutes, like this I think the first most important thing is to secure a seat. I do believe they will allow you to change your records after you get your daughter's adhaar changed.
It might also help if you visit the director of those institutes in person and get an idea of what their internal process is like (maybe get something drafted from your lawyer or HC court order if they give you trouble)
Speaking of which I recently had to change my adhaar as well, to change the gender you won't need any supporting document on adhaar.
For the name however make sure you submit only the gazette with a photo that is cross signed. That's what I had to do in order to get my adhaar changed (by instruction from UIDAI) they don't seem to accept the tgid off late. A few others like me wasted 2-3 months due to that.
This should hopefully have your daughter have her adhaar is 2 weeks time. (Took me 5 days to get the name and 4 for gender)
If you have to update her biometrics remember you can only update 2 things at a time. If they try to do 3 things it will get rejected.
Best luck.
