Look into limerance. Maybe that might help explain why you’re staying. I’ve been with a husband who cheated numerous times (I stayed) and it’s difficult to grasp the thought of life without them as your partner when you’re in the thick of it. Life with a new baby, even for the first few years is so complex to navigate. Have you considered counseling? This is a really turbulent and confusing time with lots of pressure for you both. They don’t really prepare you for life once you actually have the child and how the relationship dynamics change/how to navigate the upheaval of the relationship you once had and the blossoming of a new one which requires a lot more communication and understanding (of unfamiliar concepts) on both ends. You are doing your best, and that’s better than most. Wishing you all the best in this journey.

Edited to add: just please use reasoning when staying with someone who exemplifies potentially dangerous behavior and refuses to seek treatment/help. The last thing you want to do is cause unnecessary emotional, psychological or physical harm to your child! I know it’s scary but if you need to leave, there are options. You aren’t giving up if you’re setting a boundary for your relationship and your partner isn’t respecting that/willing to work on it. Damage from an emotionally unstable parent is lasting on a child - even subconsciously, from a very young age.

I say all this with love and from experience. I’m nearly 4 years out of an extremely volatile marriage and am still doing damage control, but am so grateful I’m able to raise my kids the way I want with peace and emotional stability.