But SOLOST what are you going to say about the "base camp" issue?
Agreeing a rota of set days is only part of the solution here. I also think you are doing his worrying for him. He's a working parent - he will have to make it work, just like all working parents manage. If that means the job he's taken doesn't give him enough time with the DCs, then he's got a choice hasn't he? The same worklife balance choices all of us have to make. If I hadn't set up my business when my DCs were young and had continued working 12-hour days so that I hardly saw them, that would have been a choice wouldn't it? If I was separated from my H and he was the primary carer, then I wouldn't choose to live 100 miles away and take a job with long hours, travel and evening wine and dines, I assure you. And I certainly wouldn't expect my H to fret about my schedule, especially if I'd treated him and the DCs so badly. You really need to reverse this situation more and ask what you'd make of this situation if your H was a woman who'd buggered off.
So I'd ask him to pick the (same) days that work for him and see if they work for you and the DCs. Remember to rotate the weekends too. As far as the DCs go, I would explain that now that Dad has started his new job, it's a good thing to get into an established routine, so that they know the days they are going to see him. Explain the benefits to them of knowing ahead of time and being able to arrange their social lives around their time with him. They'll also know lots of children who do this - as I keep saying, your arrangements are the aberration here.
But all this still won't be enough if you allow him to keep picking up the children from their home and returning at various points when activities have finished. Whatever you say, I'm pretty sure he does come into the house and can't imagine that he has gone from doing odd jobs in the house, to not stepping over the threshold, in such a short space of time.
He'll have to make the base camp work for him too, won't he, once you force the issue? It will be his problem to sort and that will make him confront the choices he's making about where he lives.
The DCs will be fine Solost. It's you who needs to take this leap - not them.