Should I allow other inexperienced riders take lessons on my daughters horse?

I am boarding our 12 yr old horse at a 4-h barn. We are doing a partial lease, we are sharing the horse. He is being used for lessons for 4-h'ers. During my daughter's lessons her seems to not want to coopertate. She I ask that no one else ride him? We are only able to make it out to the barn on the weekends. I have been told that the more he is riden the better he will me, but I have not seen the benefit.