Im so sorry to say this but your BIL sounds like a ganwaar-type. He is taking advantage of your father not being in the picture and thinking he can control your future and actually has the right to say something to you. If someone got in my face like that about my PERSONAL choices regarding my PERSONAL life, I would have laughed at them and walked away. Your mom is a very smart woman, listen to her next time.
If I were you…I would do what Niks said…cut off all contact for the time being. Do not talk to them again after today until they realize what their place is. Take your mom so she doesnt have to bear their tanay and leave. You’re independant…what are you waiting for? What do you need from them?
Leave. Dont look back. Leave them behind and walk away.