OP, that phrase "I don't want my kids to come from a broken home," really think about it. They're already in a broken home. Their parents don't have a happy or fulfilling relationship where they treat each other with love and respect.

That's not true. We are very good together. We just don't have a physical relationship.

who can or is willing to put in the work for similar intimate and fitness goal

I used to be in good shape.

Neither of you are happy in this relationship, and nothing is going to change.

I'm happy! Just not happy with his little girlfriend!

Even if you lost the weight and your husband was attracted to you again...do you think you could ever fully trust him? He wasn't just having one night stands, it sounds like this 20 year old is living in that apartment

Yes. I mean asked if he was being unfaithful and he was honest. She isn't living there, well not really. She is a student at NYU and stays there sometimes because she doesn't like her dorm. One night stands would be worse. At least he is only sleeping with one person and knows that she is clean.

An unhappy home is a broken one, and that's where you already are

Our home is not unhappy.