Try and be a little pragmatic about this. It's very hard being cooped up in a house with somebody that suffers with mental health problems, and she has been caring for you for a long time, through some pretty heavy stuff right?
She has a point, albeit badly made and badly timed. They are your family and want to share in the fruits of your success, so why are you succeeding with the bloke next door? That's ONE way of looking at it.
You can get your pats on the back here, because you should be proud of your success, just try and see it from their point of view too. There is no right or wrong here, it's just perception and feelings.