My family's gonna disown me

So a few days ago my fiance and I got in a huge fight and my daughter and I ended up leaving him. I thought it was the end of our relationship, so my family helped move us into my sister's house for a few months. Well, it's only been a few days and I want to try and make things work with him. He is dedicated to going to individual and couples therapy, giving me space when I need it, and stepping up as a father. He just doesn't want me to give up, and I'm starting to feel like I dont want to...

My biggest thing though is telling my family. I've been with him for 3 years and our baby is 4 months old. We have had a lot of rocky times in our relationship, but I think we owe it to our daughter to try. My family hates him because he has been very jealous and possessive in the past and they don't get why I cant see past it. I'm worried if I go back to him, my whole family will write me off and never be supportive of me again.

What should I do? Is it worth trying to fix? What do I tell my family?