Should I allow someone to show my mare?

I have a 5yr old arab x paint mare that I trail ride, paper chase and do fun rides with. One of the girls who rides at the barn with me has really taken a shine to my girl and begged me to let her ride her. I was leary at first as Laney was a rescue and its been a rough year but she is steadily making leaps and bounds in the right direction. This young lady has ridden with me, and even helped me with training. I have let her ride Laney under my supervision and she does very well and follows the cues I have taught Laney to a tee. She recently asked if she could take her and show her in green pony cles... i dont know why Im so leary about saying yes. I know that they will do well, but I just don't know why I am so reserved about it. Im not jealous I have no desire to ride english, I enjoy my trails and my peace and quiet. I think part of it is will this change my girls outlook on the trails for better or worse? It isn't hard to overwhelm Laney still as she was beaten a good bit to force her to do her previous owners bidding. What would you do in my shoes?