Oh, my, DOmomma! I'm so sorry you're here and that you're going through all this misery!
Although not an expert on SA (unless living with one for 22 years makes me an expert), I can tell you that your husband DOES sound like a candidate. That does NOT excuse his behavior, but in some strange way--for me, at least--it helps to explain it. Trying to wrap my mind around him, his disease, his behavior, and how it all affects me and our children is important. And it's key to our possible reconciliation.
In S-Anon, a common saying is, "You didn't cause it, you can't control it, and you can't cure it." After 8 years of hearing it, I finally "get" what my husband means when he says his "acting out" isn't about me. He's not choosing someone else because he isn't satisfied with me, because he doesn't love me, because he's bored with me. He acts out because he's an addict, because he's broken, because he doesn't have healthy coping behaviors. And each time he acts out, he feeds the cycle of shame--which compounds all his issues.
Whether you leave your husband or not is ultimately your decision. You might want to postpone a permanent decision, though, until you see if he can get himself into recovery. Ultimately, recovery is for him, but it affects you and your two children, too. He WILL be a part of your life forever because of them and you do want him as unbroken as possible. That seems unfair, but it's true. SA is a progressive disease. It starts with porn/fantasies and progresses in all sorts of directions.
My husband is NOT a deviant. He's never done anything weird--just soul-shattering to me. The dirtiest I ever felt was when he confessed (the confessions when they're in recovery are incredibly painful) that when he was in an active addiction phase, he would (TMI warning) "masturbate inside me." What a winner! What a way to make me feel special! I tell you that, though, so that you'll understand why your husband can make love to you--even twice in a day--and still be acting out. The beast inside is still not tamed. What seems intimate for you is only fulfilling a base need for him. And it's never enough.
The good news is that there IS hope and help for sex addicts. The road is long and hard. If your WH is intent and focused, though, he can do it. If not, then he can't. But it involves a CSAT, a 12-step group, a sponsor, reading. The I Can Relate link is a great place to go and to educate yourself about the reading materials for sex addicts and spouses of sex addicts.
Another truth you'll find in the Spouses of Sex Addicts thread is that--especially in early recovery--you'll NOT find out the whole truth. They aren't lying like serial cheaters--to get away with more; they're lying like addicts--to save you and themselves from the horrible shame and toxicity of their behavior. They're NOT proud of themselves. There's a saying for an addict who's not in recovery: "If his lips are moving, he's lying." So you have to read his actions--if he gets to that point. Here are the actions you'd look for and could trust:
Is he going to a CSAT? If so, there'll be a disclosure statement after a few months that will give you MUCH (supposedly all but often not) of the truth. You can get permission from your WH to meet with the CSAT and ask your own questions. To verify.
Is he going to a 12-step group? Does he have a sponsor? Does he meet with him often?
Has he given you ALL his passwords? Has he put a GPS track on his car (mine just did that for me) so you'll know where he is and where's he's been? Is he open with his computer viewing? In a place where you or your children could see what he's up to?
Every situation is different, so you have to tailor your boundaries and your needs to your husband's particular weaknesses. As for his living situation, I get the no money thing. We have none. We couldn't live separately. That doesn't mean we have to be in the same bed/room, though, or to be intimate. Even if we ended up divorcing, I'm not sure we'd be in two different houses. Our joint income is only enough for one family--and not even that.
Bottom line, protect yourself and your children, love them, continue--however possible--to get that teaching credential, do NICE things for yourself that empower you (even if it's educating yourself about SA), check out S-Anon for yourself (so, even if you divorce your WH, you don't end up with another addict), improve yourself somehow (fix ONE thing that bothers you about yourself--just for the self-esteem boost it gives and for the distraction/goal it creates).
I spoke with my ecclesiastical leader yesterday about some of the issues I've been facing recently. He was floored and is in awe of my strength. I am, too, quite frankly. Do I break down and cry? Absolutely. Do I give up sometimes? Momentarily. Do I love my husband? Yes. Still. Is that enough? Maybe not. Am I resolved that I will make it through this trial, as unscathed as possible? Of course. I will be a better person. I didn't seek this out, but I believe that challenges build character (I'm gonna need to rent a U-Haul after this!!!).
Prayers and well wishes for you as you navigate this journey. It sucks. It's not fair. It's excruciating. But you will survive, short term, and thrive, long term. Hugs!