One idea - Think about your son a little more deeply. You say it is awkward for your son, having his dad on the sofa. You think your son feels uncomfortable. Probably true. How much more awkward would it be for him to be gone? How much more unpleasant for his dad to be 2 hours away? I am no professional, but it is my understanding that for kids, the only damaging part is when there is active hostility and anger in the house between the parents. If the parents are polite to each other but warm to the kids, it's still ok, better than no parent at all. Two parents who live together peacefully and respectfully, though not with passionate love, are good for kids.
We think of kids as these delicate flowers, and in some ways, they are. But kids are people too - they are not characters in fairy tales. Kids need to see problems and troubles, and they need to see people working through them with love, honesty, integrity, and compassion. This is invaluable, because if you fast-forward in any person's life, you can guarantee there will be unexpected, unpleasant surprises. Kids need to see parents behaving with grace under pressure, so that they know this is possible, later in life when confronting their own difficulties.
I am not telling you what to do. Only suggesting a different perspective on your son. Also I recall that your son has special needs, and it's possible that all of this does not apply to him.
But listen: I see a lot of people on this board who lament the toll the situation takes on the kids. And it is regrettable. But it seems to me that parents often feel their kids' emotions for them, real and imagined. That is not our business as parents. Our kids feel what THEY feel, we feel what WE feel.
Kids are resilient. We as parents are often distressed because we relive our own childhood views. We project them onto our own kids. But my kids never were 13 years old, not yet anyway. Comparing my childhood to that of my kids' is not helpful - it only muddles my thinking. I need to be careful about that.
If you think it is awkward for your son, as you said, maybe you could talk about it with him? Rather than reading his mind and drawing conclusions.
Of course, maybe you have done this kind of thing, and your son has already said - "Jeez, I wish Dad was living somewhere else. I hate him being here." But it did not sound that way from your words "I am uncomfortable, and so is he. I think my son is also." Those words sound more like you reading your son's mind.
Of course, we all realize that it is very important to consider the kids. We are parents and we cannot act but with their welfare in mind. But in the end, it not is the kids' decision. Or to relate it to your specific situation, your son's perspective does not trump all other factors.
You also said H has to leave because I cannot move forward on this journey while he is here. This sounds more honest to me, than "I think my son is uncomfortable."
If you need H to be gone, say it and think it and embrace that fact. Do not lay the responsibility for your choice at your son's feet.
--- I feel you struggling with this situation, it is going on so long. I know it is awkward for you. Having your H half-in and half-out of your life. Sorry it's hard.