It is ok to put down the enrollment deposit if you have to for housing access. Other schools won’t know that you have done this. The idea is to only have one enrollment deposit at a time though. Also, make sure if/when unenrolling that you unenroll from both the school and from the housing…unbelievably those are separate functions at some schools.
You are right that the schools are backing students into the corner and basically forcing deposits this way, but there’s nothing to do. Good luck with the rest of her decisions.