Here is my take on it. If you are going to bring your children to the salon while you are getting your hair done, make sure it's for a limited time. If you are getting a chemical service, you may want to think about a sitter. Most children can not sit in one place for more than 45 minutes to an hour at a time.
If a sitter is not an option, then bring something for the child to do: books, video games, a toy, snacks etc. If you bring a snack make sure it's okay with the stylist if they eat while waiting and pick up anything that they leave behind.
Remember the salon owner is not being rude or mean if they suggest not bringing a child to the salon. Safety is the main concern. Please realize the salon is not a place for the child to run around and play. There are many ways a child can get hurt from falling to getting burned. There's also chemicals that can hurt a child if they get in them. The retail shelves are not something that the kids should be allowed to play near. Bottles can break and if digested it could be toxic as well as burn their eyes if it gets in them.
Another factor is you are paying for a quality service along with the other salon guest. If your child is not sitting next to you being quiet then more than likely your stylist along with all the other stylist are watching to make sure they don't get hurt which could have a not so nice outcome for your hairstyle. Remember it is very difficult for you to pay attention to what is going on behind you while your stylist is putting foils which ultimately means and unsupervised child.
Last but not least is the relaxation. Many people come to the salon to have "me time". That time where they don't have to be mom for just a little while. Relaxation for everyone is the key factor. You as well as the other guest in the salon are paying for a relaxing, quality service.
While most stylist and salon owners know that sitters are not always an option please be considerate when bringing your child to the salon. Remember your "Sanity"at Salon Sanity is a extremely important!