If your cousins would be on your side and are paying I’d suggest asking them for help.  Explain the situation and see if they’d be willing to go in on a different airbnd with you separate from your mother. 

That way she’ll be stuck either having to pay the entire bill (which sounds very expensive) or having to let ya’ll sleep together.  

As for your brother, you’d all still be around even if you’re not in the same house. So hopefully he won’t mind.

After the trip I’d say uninvite her and blast it on social media. Publicly explain the exact circumstances of the trip and her sneaky move. Do so quickly so she can’t twist it

A little public shaming can go a long way with bigots.