Since you are the one working, I would NOT move unless YOU want to. Not when the whole relationship is so dicey.
Sounds like he should be attending SLAA meetings (sex and love addicts anonymous). I have a friend who attends them, and she says there are lots of porn-addicted guys there. They are like AA meetings.
I agree with the others, no unprotected sex with him. Plus he needs to give you complete transparency - access to his cell phone records, computer passwords, etc.
Meanwhile - may I ask what your history with him sexually is about? Were you never very interested in sex, or is this a postpartum thing, or has his not-working turned you off? Does he have a history of depression, drug use, gambling or other addictions?
Also - if you are not sure you can trust him with the baby, have you considered getting one of those babycams to see what happens when you are gone?
He's going to go back home the end of this month. I'm in graduate school doing my internship and will be done in December. He's going ahead because, after he ignored my warning in February that we would come up short on bills this month, we don't have rent money. My son and I are going to stay with my aunt and uncle here in town.
I am going to suggest he attend some sort of addictions meetings. He needs them if he's going to salvage this marriage. I have thought about complete transparency, but he's sneaky enough to go behind my back and do more now that he's going to live six hours from us. I don't trust him, even living in the same home.
In terms of sex, we started off okay, but, recently, I've been dealing with an assault that happened in 2003 (which he won't allow me to effectively deal with since he still wants me to have sex with him). That coupled with the way he's been treating me has turned me off. I don't want him to TOUCH me anymore.
The whole thing is just a mess and I am beyond being frustrated with him. There is so much more in addition to what I have shared on this site.