I would say talk with both your mom and your neighbour. Yes it will be a heartbreak for your mother but it would be better than catching them in some act in the future.
Edit: I read that your mom was the main earner. In this case, I would say wait till you finish your college, get a job and move out with your mom. Expose it to both your mom and neighbour then.
Always remember. Once a cheater, always a cheater