OK you have to buy yourself time - don't worry about principals your situation is far too precarious right now, effectively you are being blackmailed and you need time until you are ready to SAFELY move on with your life.
Baptism should be avoided at all costs, it will complicate things later and as u only have one functioning parent AT THE MOMENT try to keep things as calm as possible.
Its a good idea to mention calling in the elders, say your fear around your mum is affecting your mental state at that u have to be sure you are not going to betray Jehovah by ending up like your mum. Say u know alcoholism is genetic so your fears are grounded. Yes its BS but if it buys u time till u get finish your education and move out, in other words gets your dad off your case for a bit its all good.
And please DO reach out to your mum, do it safely but do try, if u can. Goodness knows what she has gone thru with this cult. She needs help, perhaps if she knows you will be waiting for her if she cleans herself up it may be the motivation she needs. I don't know your situation of course, but I do know noons becomes a homeless alcoholic unless they are hurting like hell.
Anyway do anything u can to buy time, talk to a school counsellor and check out Secular refuge/safe houses.