Rearing is an incredibly dangerous habit. A horse that loses its balance rearing can fall over backwards on its rider which results in very dangerous injuries. I apologise for worrying you but you should be worried.
Has your instructor assessed this pony as suitable for your DD? I would never buy a horse without input from my instructor, it's always wise to have a second opinion from someone experienced who is on your side.
Did you have the horse vetted?
You have two options:
- cut your losses and return to the dealer asap for a refund. From what you say the pony does not sound like a very good deal, e.g. out of work for a while, difficult to handle, etc.
- deal with the issues.
If you decide to deal with the issues, check some basics: is she out 24/7, is she on as little food as possible? Does her tack fit? Handle her yourself until she settles. Lunge her to get rid of excess energy. Don't feed her treats for no good reason, especially if she looks for them. Do reward good behaviour, such as standing still, with treats but teach a 'leave it' command first (as you should always do when working with animals and food).
I would also suspect you are winding her up a bit by going from the field to the stable, to the school, to the stable, to the field, to the stable, etc. If you want to ride her, then bring her in, ignore the moving around, tack her up quickly and quietly and then ride her giving her a job to do so that she concentrates on the rider (she may need a more experienced rider than your DD though, at least for the first few times). Then turn her out.
To be honest you sound a bit inexperienced in your post (apologies if I misread your post!), and this does not sound like the right pony for you.