Absolutely LOVE this idea! It's a beautiful tribute to your mom, it's personal and perfect.
I hear you about the money, you don't have it and that's hard. A free tattoo from someone in experienced is more likely to look awful, age awful and get overworked or infected. There are ways round this though!
You could ask for tattoo vouchers for Xmas and birthdays, enter competitions online/dog walk etc to make extra cash, and contact artists you like to see about discount days. Quite a few will do it cheaper slower times of year, during promotions or even discount their rate to do a meaningful one.
Definitely look into that first, that way at least you know you've tried.