If you got chickens just because and you don't even like eggs, then maybe you're making a mountain out of a molehill?
No, she probably shouldn't be just taking the eggs, but in the end IMO it's not worth jeopardizing your relationship with your boyfriend and his mom over some eggs.
Maybe have a talk with her and split the number of eggs between your family and his? You really aren't going to have that many to sell with only 5 chickens anyway. Maybe your folks can pay X amount per dozen to help out with the feed and you can consider the ones going to his mom as paying the rent for the coop.
You say that your boyfriend maintains the yard, but hey, he lives there and I'm guessing mom pays all the bills, right? The yard work should be considered his contribution to the household, nothing more.
If I were in your position and it got to be a problem, I would rehome the chickens and be done with it until I had my own place to keep some.
Best of luck with whatever you decide to do