EDIT! Sorry, just saw your post but posting this anyways!!
I would confront the parent, preferably with the child. Say, I would like you (adressing the parent) to be out with your child whenever he\she is here. Are these horses yours? Im a little confused on whether you are meaning you are letting them come out and ride without supervision or if you are letting them ride your horses. Also it may be a good idea to tell the parent\kid that 'you need to be taking lessons with a good instructor, whether it be me or someone else, because I want you to be safe riding your horse.' If it is your horse, you need
to say that they have to take lessons to be able to ride this horse because you want you and the horse to be safe. Good luck