Um, I haven't had time to read all the comments but OP, you did cross the line in assuming it would be ok to stay with them. THEY HAVE A 1 MONTH OLD INFANT.

Babies that age don't sleep. I think you are catching them at a very stressed, 'we're losing control of EVERYTHING', hard time in their lives. Basically when you have a kid, it's normal to try and over-control other aspects of your life because it's such a change (especially when you are inherently controlling). Have a little compassion for his perspective too. You may not agree, but you can do something to avoid arguing over it: stay in a hotel.

I think you should visit and stay in a hotel. Is this worth losing your relationship with your brother over? If his only issues are where you sleep in the house, then visit. Take over baby duty so he and his wife can go out to lunch. Bring them dinner and meals. Help out with laundry and cleaning.

I'd also take your mom's opinion with a grain of salt. It's never a good idea to mediate through a third party. Certainly keep your distance from your brother, but alienating him completely? Over this? Is it really worth it?

Once the baby gets older and ESPECIALLY if they have another (if they are religious, they will probably have lots of babies), you will have the opportunity to develop a close relationship with your nephew. First your brother and SIL will have to get over the 'first child paranoia', but they will out of necessity. You and your brother don't have to agree, you just have to both agree to disagree and behave accordingly. But creating drama when your brother has a young infant isn't really going to help anything.