It really does! I spend a lot of fresh produce for them. I've tried to find local grocers who have stuff they can't use, but more often than not it's no (they have a local waterfowl rescue that picks up which is awesome). I'm about to add oyster shells into my expenses since I have a roo and it's a bad idea to switch to laying feed from what I was told.
I agree with time and costs. If you're winning shows it would help, but it's a big investment getting there. If you are selling eggs, it could help with money, but again it's an investment and more birds.
The best information given though is about research and knowledge. Get books from the library that your mom can thumb through too. Make lists of pros, cons, and household benefits. If your mom gardens maybe she'll like the access to manure, maybe she'll appreciate a decrease in food waste? There are many benefits to owning a chicken that aren't obvious ones, you can research to make your case. Be patient and thorough, take the time to prove you're dedicated, whatever you do don't argue with your mom. Invite her to learn with you.