You think your husband should love and respect you for doing lots of very difficult mum things. But as difficult and worthy as those things are, you're not doing them for him. You're doing them for your DC and if you separated, you would continue to do them because you love your DC more than anything and your love for them is not contingent.
You don't have the headspace or inclination to do any wife things, and you think your husband should understand. You married him, and you gave him children, and he should just get with the programme because this is what life is now. You're parents. Your kids have to come first.
Your husband wants you to do wife things. You aren't doing those, so he's sulky and resentful. The sulkier and more resentful he gets, the even less likely you become to do wife things.
He doesn't think you should both be defined by your identity as parents. He wants that relationship you had before the kids where he was the most important person to you. Again, this seems unreasonable to you, so you push back, and he gets sulkier and sulkier.
You're trapped in this spiral of resentment. I have never seen a couple bounce back from it.
Your needs are not being met as your husband does not value your identity as as a mother.
Your husband's needs are not being met, because you do not value his identity as a husband.
Would therapy teach you to prioritise time for yourself as a woman and a wife? Well, not if you can't find reliable childcare for your children (if you're a carer for one of them, getting the right paid help is going to be a challenge). Therapy can't suddenly make the practical obstacles in your life easier.
Would therapy teach your husband to accept he's no longer a 20-something and has family responsibilities now? Well, if he can't get sex in his current relationship, it's not going to stop him from looking elsewhere and getting it elsewhere.
Couples counselling in your case is only going to help you both prepare and adjust for a split.
I think the best thing you can do now really is to discuss how you can effectively co-parent your children and move on amicably.
Alternatively, if you can't accept that... could you ask your ILs for respite help with the kids, making clear that if they don't help you, your marriage is likely to break up, as you're in the last chance saloon trying to repair things? If the kids get on with them, I wonder if they could help look after them temporarily so you and your husband can spend some quality time together figuring out if there anything left there between you other than the link as parents.