Dearest OP, this is far from a healthy relationship as it seems that he keeps you just that bit too tired and overwhelmed and shows just enough "niceness" to keep you from thinking clearly.
You think you still love him but isn't it more true that you love the man he could potentially be if he actually cared and put in the effort? Believe me, even if you saw some of that at the beginning of your relationship, you aren't going to see it again, at least on a permanent basis. I'm speaking from both personal experience and observation of others relationships.
It appears from your posts that you are in an abusive relationship. Just because he doesn't hit you, doesn't mean it's not abusive.
Please contact whatever domestic violence helpline you have in your country and speak to them. Or if you have a sympathetic female GP, talk to her.
Wasting food in a sulk is abusive behavior.
Making the children upset, afraid or cry so that you step in to do the task is abusive behavior.
You being afraid to ask for a discussion about what reasonable co-parenting behavior looks like, because he won't have a discussion without turning it into a shouting and slamming doors situation, sulking, martyrdom and possible withdrawal of the minimal effort that he already puts in, is abusive behavior.
Demanding and attempting to guilt you into sex instead of ensuring that you feel energetic, attractive and attracted so that you are enthusiastic and enjoy the act, is abusive behavior.
Do you have any money of your own that he doesn't ask you to account for? Do you have to justify even small spends? Are his wages "his money that you're spending" or is it family money with both of you having equal access and responsibility? If it's the former, that's financial abuse.
Has he ever been away for a couple of days and the house felt calmer, lighter?
Would you wish your type of relationship on your children?
What would you advise your child to do if they found themselves with a partner like yours?
It sounds like you've already tried talking to him and you've tried counseling, neither of which have worked long term, so the person with whom you're living right now is the real him, because the considerate him is only available on a temporary basis at best, after a lot of effort on your part.
If splitting up is the only healthy solution, there is assistance out there. Work on your mental health. Find a good therapist. Start putting by some "Running Away Money". RAM has always been a good thing, even in healthy relationships, as it gives the woman a sense of power over her life, even if she never needs to use it.
Good luck OP. I hope the responses you're getting here are helping you to think about what you and your children need and how to achieve that.