I whole heartedly think you need this time for yourself so that you two can work on being a team but I would actually reconsider your instructor's offer concerning jumping. You don't want to learn or relearn to jump on a horse that there is a question about. I don't remember reading if that was part of her career pre injury or not. Either way it may be worth it to see a good, experienced (currently) rider take her over a few for an evaluation by you and your instructor if she has been jumped before or by a good, experienced rider capable of teaching a horse to jump if she hasn't under your instructor with you there. Does your instructor train as well as instruct rider's? What is her level or is she that confident in her daughter and her experience that it would be a good fit to see what your mare can do? When you are both comfortable with you and the horse's ability then move forward and jump together. I have seen some disaster's (like call the ambulance and person is hospitalized with serious injuries) with riders that aren't ready on horses that don't really know what they are doing but they were adamant that they wanted to be a "bonded" pair so no one else was allowed on the horse. This wasn't on jumps over 3 foot. They were under.
I don't know if your month is up but if it isn't then evaluating this and then seeing how she responds physically in the event she does come up lame from it as long as you have a return guarantee would be worth doing. Unless you have decided that even if she weren't able you would still want her for trails or ring work.