He wants to stay near his children and wants to remain in their life but says he feels disconnected from me but wants to be in my life
That doesn't sound like a very appetizing offer. Particularly not when it's in such wild opposition to the vows he made to you.
You know, my WH made the same mad claim... that he was "disconnected". And then he went looking for NSA sex, which of course is NO connection.
It's bizarre how their minds work when they're cheating. It's like they don't even hear the idiocy coming out of their mouths.
Anyway, I agree with all those who have recommended that you see an attorney and find out what divorce looks like. It takes TWO to reconcile, and both parties have to really want it. It's a helluva lot of damage to overcome, and lukewarm commitment doesn't cut it. Perhaps if your WH understands that you're not going to accept less than the 100% effort you deserve, he'll wake up and apply himself. And if he doesn't, you're well on your way to a cheater-free life.
I will share this with you though... Shortly after my own DDay, when my WH was still "lukewarm" in his desire to R, I remember having a conversation with him about what kind of relationship we might have in reconciliation. Basically, he was trying to figure out if I'd ever let him into my bed again. I looked him right in the eye and told him that yes, I did intend to have an emotionally and sexually intimate relationship with a man again... and if it wasn't with him, it would be with someone else. Bam! Have you ever watched a person's face closely when the penny finally dropped? It had never occurred to him that I might divorce him *AND* find someone new for myself. He thought I'd just grow old, bitter, and dusty pining over him for the rest of my life.
Next time your WH gives you some lame bullshit like "he still wants to be in your life", tell him straight up that once he's out, there won't be room for him. You don't plan on collecting dust, waiting on some shelf. They don't expect us to be strong, sweetie. They expect us to shrivel up and spend all our time crying. It's startles them when we show an aptitude for moving on and putting them behind us.