Massive 
to you.
Your marriage sounds very much like mine; and we separated three years ago when our DC was two. I am not going to go into detail, but I feel your pain.
Here is what happened.
H did not accept that I wanted to separate (it was a cheek on my part, apparently). The difference was that the house I lived in with DC was mine, as he had not ever parted with the money or the time to help sort out a joint family home (and was not happy with what I had); and he was there physically less than your DH is, and minimal 'help' with anything. All complaints on my part were met with, it will be fine when we have a bigger house; but I could not see how this solution was ever going to be met if I was working FT with the DC and no support and he was not doing anything on the house front.
I asked him to stay away, and only come to the house for contact at weekends with DS. I let him use the house initially for this, but after about six weeks, it was clear that the time was also spent harrassing me. So, at that point solicitors got involved and it got messy and expensive; and I think it cost over £1k just to get him to engage a solicitor and accept that the marriage was over. Actually, it was ten months of harrassment hell and trying to arrange contact with DS in a neutral location.
However, at the same time as all this was going on, H did manage to get himself a flat sorted out double quick (despite not being able to shift in five years on a joint matrimonial home with me). He has bought it as a second home and investment, after having taken legal advice that I would not be entitled to any of it as I had started proceedings against him, and we were separated - so it was as much a clever way of hiding assets as anything else - after all, it was a flat where he could see DC, so what could I say??. Nothing, because in the end of the day, it did benefit DC.
I then argued for daytime contact until DC was able to do overnights. he really does now spend time with DC and they have their little routine worked out that H manages to cope with. Their relationship has blossomed, but honestly, there has been a LOT of work on my part to make it manageable as DC has various needs (in the process of seeking a diagnosis), so the transition to overnights was not smooth (and still has not happened).
We are communicating better, which is good for DC, and we have approached reconciling, but the more I have gone down that route, the more I realise why I left the marriage. It makes me very sad, and I am not sure what will happen. i think the best outcome would be that we co-parent amicably, we are still friends, and that he and DC have a good and solid relationship. I am not sure that ressurecting our marriage is possible, although he would like it.
That is a long post, but I hope it helps. It is hard work getting out of a marriage to someone who does not believe that you have the right to end it, because you stop believing your own instincts.