If you can convince a vet to help her, they just need to push it back in. Send them the picture, and also if you Google " bearded dragon prolapse pictures, there will be at least one series of pics from an actual procedure that even a regular vet should be able to follow. You can plead with them ! She should have some sedation, I'm sure they could figure it out by weight as to how much to give her , or at least some pain meds. If none of them are willing, then you must push it back in. I have done it before on a younger dragon, it was not as severe as yours but it DID go in. But I think if you were insistent that a vet would see her and get it done. Once it's back in thet put in a couple of sutures.