How do I get my 10 month old to stop needing to feed twice a night?

You will have to slowly wean him. Start doing it only one each night instead of twice and eventually bring in a warm bottle and snuggle him until he is used to the bottle. As for the screaming competition, that will be a normal part of weaning. Babies cry to get things they want so that will be inevitable. Maybe you could move your 2 year old into your room or the living room until your baby can get settled.