I don't know how he expected that committing adultery would improve your marriage, but yeah... I think I'd go ahead and turn this thing around on him by booking MC. Here's the deal though... YOU interview and select the therapist. It sounds to me like your WH needs to GROW UP. You are not his personal groupie or cheerleader. He's a grown man and he should be long past the need for praise and flattery. And as far as sex goes, he should be capable of negotiating a reasonable sex life using his big-boy words. 
You've got children to take care of, including another infant, as well as a new business to run. And I'm not saying you shouldn't be making an effort in the marriage, but it's not going to be the "WH Show" 24/7. You're only three years into R. The wounds don't typically heal that quickly. At this point, you're most likely still having trouble maintaining an emotional connection. His stupidity here, moving out of your bedroom and sulking like an infant, has undermined what recovery you've made. (Ugh.. if you can't tell it, I'm just incensed on your behalf! 
)
Anyway, that is what I would do. I'd haul his ass into the MC of MY personal choice... where we would talk about what are reasonable expectations for an ADULT to have and how he might make better use of the chance for R that you have given him as a GIFT. No one is owed a second chance. He got one, and now he has practically thrown in back in your face.
I'm going to reprint a post I made for someone else about the "unmet needs" fallacy and avoiding those kind of therapists. Don't be afraid to thoroughly interview. You might even go to the first meeting on your own just to make sure.
My own WH went on a Craigslist binge six years ago, multiple partners, various degrees of emotional attachment. He even thought he was in love at one point. But ten years before that, I'd caught him out in some online shenanigans, porn, cybersexing, emotional affair, etc. In fact, I caught him out only two weeks before a planned meet-up. I'd already seen an attorney before I confronted him and I was bent on divorce, but he pretty much cried his way out of it and I settled on MC. As you might have guessed already, we too were bamboozled with the "unmet needs" model of therapy, which sounds so reasonable. I upped my wife game, and did my best pick-me polka, but within a couple of years, he was right back at it behind my back. By the time we reached the ten year mark, he had screwed up his nerve to go live and in person on Craigslist.
Of course, I was pretty shocked as you might imagine. I thought we were good. I thought his "needs" were met. Damned if I hadn't been turning myself inside out for a decade to make sure, right? The more I thought about it, the more I revisited what I knew about the "unmet needs model", the less it made sense. I was doing everything right and he still CHOSE to cheat.
Here's the fly in the "unmet needs" ointment...
Healthy ADULTS don't need to be validated. They validate internally. Healthy adults are self-fruitful in the matter of contentment and life satisfaction, and when things come up which make them unhappy, they address the cause and solve the problem. OTOH, the vast majority of cheaters cheat because they're seeking external validation. They are NOT emotionally healthy. They can't do it on their own. They've got a hole inside them and no amount of external validation will fill it. Certainly, the old and familiar validation of a spouse doesn't get the job done. Our "kibbles" are stale and boring. They don't create enough adrenaline anymore to make the cheater feel special. It's like getting an "atta boy" from your mom, right?
This is old pop-psy which is still being taught in schools and still selling books. But it's bullshit. NOTHING you can do (or fail to do) can MAKE another person throw away their core values and do something that's in this kind of opposition to good character. If you're a person who BELIEVES in fidelity, who VALUES fidelity, you don't cheat. End of story. Because when we truly value something we protect it. The cheater has a "but..." in his values system. ie. "I believe in fidelity, but... not if my needs aren't being met." For people like you and me, we have a "so..." in our values system. ie. "I believe in fidelity, so... I don't put myself in risky situations with the opposite sex." This is the BOUNDARY we create organically. We don't sit around planning it out. It just happens, because it's innate to our character to protect what we value. The cheater doesn't have those boundaries because he doesn't really honor his values. He only claims to.
I'm not saying that your marriage is over or that your WH can't change. What I am saying though is that this "unmet needs" model is NOT going to challenge him to clean up his flawed character. In fact, it allows him to offload responsibility onto the marriage and onto YOU. It's not your job to MAKE him feel (fill-in-the-blank-here). It never was. It's his job to control his feelings. You could have been doing everything exactly perfect for the entire length of your marriage, and he would still have cheated... because there's NOTHING in his character stopping him and he has no coping mechanism to fall back on when he feels unvalidated, inadequate, unappreciated, etc.
It's HIS job to see that his "needs" get met. Sometimes that might mean negotiating with you, say if it's about sex or about the division of labor in your home, etc. But sometimes, it might mean that what he sees as a "need" is unhealthy in an adult, like external validation through attention and flattery.
MC's are there to treat the marriage. The marriage is the client. So, of course they're going to talk about communications, resentments and expectations. The MC doesn't want to alienate anyone, so s/he's looking to find balance on both sides. But marriages don't cheat. People do. The only way your WH is going to make a change that safeguards against further perfidy is by correcting his need for external validation and becoming an emotionally healthy adult whose deeds are as good as his word. No excuses, just honoring the things he claims to value. For that, I would recommend IC (individual counseling) with a therapist who is well-versed in adultery.
The last thing any newly-minted BS needs is to walk into an MC's office, believing that they've come to safe harbor, and being handed a copy of The Five Love Languages or some other "unmet needs" gobbledygook. It would be really nice if we actually did have the power to control our mate by giving them "acts of service" or "words of affirmation", but sadly, we aren't gods who can stop a cheater from seeking out his/her choice of adrenaline rush and new kibbles. Although, this kind of pop-psy suggests that their behavior is somehow our responsibility. The more you dig into this ridiculous line of thought, the more absurd it becomes.
Anyway... sorry for the lengthy post. Nothing fries my ass more than seeing new BS's being sold this bill of goods.
R is still going fairly well.. 7 years now. I consider myself healed.
