Two scenarios: a) Aya cares about Cain. Therefore, since it wasn't her burden in the first place and Gym substitutes are probably bound by contract, while receiving certain benefits (or just... pay) when having proven their worth, she took the job that otherwise would have stopped Cain in his tracks.
They need the money/position/place/gym. As stated above they probably receive certain boosts, either economic or territorial (having a free house or area under command, which they can do whatever they want with). Her mother, being the bitch she is, is probably unemployed and lazy, must be having a hard time dealing with stuff (probably after a fall of the father) and they do their best. It would be interesting to get some insight to them. It's not used in pokemon games, but Reborn has always been different.