As in all things, no therapist can help unless the patient wants it.
Honestly, if he has no job, the kids should be taken care by him. idle hands, idle minds, idle time = trouble.
From a prospective of a guy who cheated on his gf, let me tell you a few things.
1) His affair, regardless whether he actually met anyone, is still cheating b/c you didn't know about it.
2) Him cheating on you isn't your fault. There may be issues to resolve between you two, but him cheating on you was a choice he made, regardless of the reasons.
3) Instead of dealing with whatever issues he had when you were pregnant, he chose the chickenshit way out and not confront you and sought out the excitement/contact of another woman. I know this, b/c every time i'd get into a situation where my gf and I weren't doing well, I'd attempt once or twice and give up and go find self esteem / easy feelings from someone else.
4) all affairs are fantasy. it involves real people and victims, but the relationship is illusion b/c there are no diapers to change, no reality in it, other than the fantasy of attraction and chemistry.
5) I realize you're married with two VERY young babies, but if you want your marriage to actually work long term, you need to get on his ass and give him a choice. Do the couples therapy or leave.
There are resources online that can help people in your situation to deal with spouses like him. I'm thinking even he doesn't know why he's tempted so much. Therapy only helps those who desperately want it. Does he desperately want the marriage; whatever good feelings he has outside the marriage... it's just an escape from the reality of it. Even if he divorced you and found someone, it doesn't change the source of the problem: him.
So if you're serious about this relationship... i know, you're married with 2 toddlers... then you need to be the partner he married and do what's good for him. Force him and push him, and prod him to realize what he has to lose if he doesn't get serious about repairing the marriage.