One side it trying to force them to choose a side. It is up to adults to say “this is between us, and our relationship doesn’t change your relationships.”

OP could be very supportive of their mother and still not want to move out of the home they already lived in. But it doesn’t sound like the mom wants to let OP do that.

Also, from their other comments, their father has been more supportive through their life while their mom has been cold and judgemental. Trying to force her child into a position whete they are expected to mete out judgement as well just emphasizes that they aren’t terribly concerned with the well-being of their child.

And anyway, if you want support, you should give support. And OPs mom missed that boat, so it makes sense for OP to stay with the parent who supported them.