As far as the lease vs her purchase, I agree that lease is a better option. It sounds like you already have options for a potential sudden extra horse. The reasons to buy and have her lease:
-you have control over the horse that is picked, rather than them showing up with a horse they just think is perfect but most decidedly not- whether or not they ask you to help look for a horse, you cannot control them seeing something randomly online or having a friend of a friend say, “yeah, got the perfect horse (that I want to unload because it’s crazy and you people look naive enough to take)”.
-You can assert control over feeding, farrier, etc - your horse your rules. (I used to get into it with my former trainer over my horse and would sometimes flat out tell her when I was riding her horses it was her rules but this was my horse, my rules).
-You can assert control over training/riding (if needed - we has some lesson horses that had
no jumping or no jumping over 2’ rules due to shady soundness - could they? sure…will they break down very quickly? Most likely).
-Less immediate pressure for Mom and daughter, less stress over what to do with daughter losses interest or college gets in the way, etc.
-Less stress for you - you got something you already have a future plan for, you aren’t stuck with an extra horse unsuitable to you if daughter looses interest. Mom trying to get you to help sell or trying to get you to keep etc.
Good luck!