My dog was the same with my DP and DS. the trainer I contacted to start with was... less than helpful so we just kind of muddled through it and he now only barks at them when they come in the house, which we can live with as he’s fine with them the rest of the time, well better than fine, quite happy to be with them.
With DS he threw treats to behind the dog every time he came in a room or had to walk past him, so the dog had to go away to get it. Then built on that.
With DP it was him taking over all walks that did it, he absolutely loves going out.
I’m not saying do those, but, more mentioning what we did because we did in fact do two completely different things and they still both worked - so if you can get the behaviourists plan to work fine you, it should work.
Can he shut a door to stop the dog running in ahead of him?
And you should have follow up from the behaviourist as well, so if you’re having issues then you should be able to go, um, ok, what do I do when he runs back in before DH makes it in the room?
It’s a really hard one to live with, I considered having to give mine back because of it and like I said, not my first dog and not my first dog with issues. As it was, I ended up giving him a deadline (in my head) and he improved before it and he is now happy with them other than a few barks when they come in the house from somewhere.
If you decide you’re just not equipped for him, there’s nothing wrong with that, yes it’ll be unpleasant and yes it’ll be hard to explain that to your D.C., but it is a really hard issue to live with and it’s fine to go, you know, I’m out of my depth here.
That’ll all be a bit waffly, rofl, I’m awake in the middle of the night not well, but hopefully some of it was helpful.