Should I be making my daughter get back on her horse after falling off?

My daughter is 10y/o. She has loved and been taking english lessons for the past four years on a 13hand pony. We bought land and moved to a new area and joined the 4-H drill team in our new area. She was having a great time on one of the drill team members horses but then that member needed to sell her horse for some extra money. I decided to let my daughter ride my 6 y/o gilding, who has been used for hunter/jumper. I have had him since he was three weeks old, due to the death of his mother, and I trained him myself using Clinton Andersons teachings....so I really know this horse. He is not a mean or hateful horse...he is a good horse, but young. The second week she fell off - at a canter. I did not see the fall but she hurt her arm pretty bad and it took about a week before she could lift it again. She refused to get back on him and has still not done so 10 weeks later. She has howerver been riding my mare at drill team who is 15y/o and is a been there done that horse. She says she is still nervous and does not want to go to drill team because she does not want to canter. She will get on and trot but only when I tell her she is part of a team and we have to do our part by practicing...I go out with her and she will get on and W/T only. She wont go on a trail ride with me or even out of the arena. She is so nervous and I am not sure what to do. You can see she wants to be around the horses, but does not want to get on. I am making her get on. Am I wrong for this? I told her when she can work her way up to cantering again with out freaking out I would let her make the decision to stay in drill team or to drop out. I told her I did not want her making this decision out of fear because she would run away from what she feared for the rest of her life. I really had good intentions with this, but as any mom I am really thinking I am hurting her rather than helping her. Please, please help me do what is right for her. I do not have all the answers and I really need some help. I do not want to end up killing what she loves the most, but I also do not want her to be so freaked out and crying herself to sleep after every drill team practice! This is killing me!!!!! I do have the option of driving back to her trainer once a week for lessons on the 13hand poney she uses to ride. It is only about 45 min. away. I did not know if that would be taking her back instead of going forward. I am not a trainer, and really just dont know how to handle this situation so please dont think I am being stupid by not having the right answers...I am just a mom who has not idea what the best way to deal with this situation would be..