My (new) hairdresser's business is that of a "traveling hairdresser".?

She works three days a week in a shop where she "rents" a spot then travels two days a week to people's homes to cut hair. Her traveling price is $10.00 more than a cut in the salon. Do I tip her when she comes to my home? She gets to pocket all of the money as opposed to having to give half to the shop owner when she is in the shop.

i would give her a very small tip, like a buck or 2

tough question. go with a smaller percentage like 10%, or try booking with her at the shop and tip normally. and no hairstylists get to "pocket all the money." they still get only a percentage of their earnings with the rest going to taxes and supplies