My mommy helped with all of the births of her grandchildren! She willingly flew from AZ for all of the premature births of my babies. She stayed for a couple of weeks to help me, and then she flew home. Then my MIL would come down from OH to help for another few weeks. It was a hectic household, but i appreciate all of the help that I did receive. When my last child was born, I had a 2 year old, and a 1 year old, at home. Before you ask, yes I'm done having babies.
When my brothers eldest boy was born, my ex-sil couldn't change a diaper (she's a spoiled *****!). My mom had to show her how to do everything. Four years after my nephew was born, they were divorced, and my brother became a single father. He raised my nephew without my ex-sil's evil influence.
Then my brother married the love of his life. She's a gal from southern Ohio! They have two children together. She had been raised as an only child on a farm, and she knew nothing about babies, but she was willing to learn. So me & my mom flew out to Colorado after my second nephew was born. A few years later my brother & sil had my niece, we flew out again. When my niece was a few months old my brother severly broke his leg. My sil couldn't manage a two story house, a diabetic uncle that lived with them, a grade schooler, a preschooler, and a newborn on her own. I offered to help. My husband was deployed at the time, and I didn't have any kids. So I went to Colorado and helped out around there for 6 weeks. It was the best time ever! That's what families do, they help each other when it's wanted & needed.
You can get some needed sleep if you get a co-sleeper (arms reach co-sleeper) a pack-n-play that can go right beside the bed. You can be right there with him, and get some needed zzz's. When my babies were little, I got the "Angelcare Monitor" system when they came home from the NICU. They were all born early, and I needed to sleep! This was probably one of the best investments that I ever made. It allows you to keep baby close by, and still be able to know that their movements are being monitored by this fabulous machine. I don't have mine anymore, but I can tell you that's it's an awesome thing to have.
Just one more thing. IMHO: It's NOT right for a mother to favor one child over the other. My mom never did this with me or my brother. We don't do this to any of our children. There is NO shame in asking for help. You're obviously anxious, sleep deprived, and worn out. When your hubby is home take naps. I promise it does help. Good luck, I hope this helps.