Choosing which parent to put on an SFE application

I have put my mum on my SFE application for the last two years because I lived with her, but she earns considerably more than my dad who definitely earns little enough for me to qualify for maximum loan.
If I, let’s say, had a falling out with my mum and ‘moved in’ with my dad and put him on my SFE application would this be queried? The criteria seems to just be to put the parent you are financially dependent on (both) or the parent you live with the most (how would they know).
Anyone had any experience with this because I really could do with an extra three grand a year.