Oh fozzie, I really feel for you. some of this sounds pretty familiar as well.
It sounds like you're working really hard to keep things together for you and your family.
I normally don't try to say things that include 'shoulds' but I think your husband really needs to get proper help with his depression. From what you've written, you are getting the brunt of it and relate appears to be only doing half a job. If you don't want to stop going to relate, and I totally understand why if it doesn't feel right (to stop that is) then would he consider going to a private counsellor?
Of course as amaya said above, it is his responsibility to deal with it. You can't fix him and it sounds like your quality of life, and your kids, is really suffering at the same time. Of course he's not choosing the emotions he's feeling, but he can express them in a way that doesn't make you and your children feel so bad.
However, it doesn't sound like that is going to happen very soon, as he seems to be pushing 'blame' on to you. Not that there is any blame - perhaps he's fearful of his own emotions and facing up to them- it can be really scary to admit that there's a problem, especially one so long standing. My partner has suggested we break up in his darkest moments, and this seems to be a pattern in depressed partners for various reasons. In my experience, and I'm not saying it's the same for you, it feels like he's pushing me away but it's because he's struggling to cope with his feelings of low self worth. Maybe the reason the relate councillor suggested a break, was that in your case that a break might do you all some good, and help encourage him to seek help for his depression?- Is that similar to what your Relate councillor said?
My partner also hates it sometimes when I suggest things I think might help- like seeking help on Sane or Calm- mainly because he knows they're already there- and can react quite badly when he's feeling particularly anxious or depressed. There is a certain degree of letting them know you're here for them, but also 'letting them get on with it'- which I know, can feel really hard sometimes when all you want to do is help. Sometimes help comes in the form of allowing them space to feel what they're feeling.
I'm sorry if any of that sounds like enabling him to talk to you like dirt, that's not what I intended. I find it difficult to be concise about this subject matter, as you can imagine. What I'm trying to say is that, of course you have sympathy for his struggle with depression, but you need clear boundaries for you and your kids.
It sounds like you've got an awful lot on your plate so please, please, please look after yourself. Are you seeking counselling for yourself? Remember you're only human and it's natural to find this tough,it is really really tough, but don't think you have to deal with it alone. I hope that's helpful, and not to wordy- look who's going on now!