The makeup of the "normal" family has changed, and that means stable owners might need to change some of their traditional notions and paperwork. In decades past, mothers brought their daughters (and sometimes sons) to take riding lessons, or dads would drop a teen daughter at the stable where her horse was boarded.
Today those caretakers might be the grandparents, which has its plusses and minuses. On the plus side is that many of the grandmothers are horse people themselves, or are of a generation that was more familiar with horses. That means she could be an advocate for keeping the granddaughter active in riding, or she might even be footing the bill!
On the other side, whether the grandparents have the authority to sign children up for lessons or sign your waivers could be a legal problem.
Some of these issues you will need to take up with your attorney and/or insurance agent; others you need to determine what your policy is for your equine business.
Older women and younger girls seem to make up the bulk of the equine industry. While older women present their own specific needs at a stable, the younger girls might create more legal problems for you.
You need to ask the grandparent if they are a legal guardian of the minor child. If not, they will need to take your paperwork with them and have the legal guardian sign it.
Sometimes grandparents have legal guardianship for minor children, but if you have any doubt, make sure you ask. The liability issues are not worth the risk.