Where and what would she hack out on girlie? If you have access to that, then that seems a good option. Your DD is experienced enough to handle a safe pony round a safe route without issue. To be honest, lots of folk are completely happy with that, I think that I would be personally.
But I remember your DD loving jumping too, and loving the shows.
Remember, not all lessons come from riding schools per se, DD still has lessons (and so she should, you never stop learning) at a standard livery yard. £8 for 40 minutes with a better instructor than most of the riding schools. Phone a few livery yards, you might strike lucky. This is on a small working farm.
If you are extremely fortunate, you might have a branch of your Pony Club that has municipal (for want of a better word) ponies. These are rare, but not unheard of.
Often, there's Facebook sites too or pre loved adverts where folk want their pony exercised because they can't for whatever short term reason. There's 2 on our yard that are saints and woefully underused.
It boils down to what your DD wants.
Pm if needed, I'm away still but will pick up Monday latest xx