It really does sound like he's told his family that you have split up, hence why he blocks you and not the kids, but then blocks the kids if you use them to contact him.
You've not seen them for 7 years, and he's been acting strange for 4. I bet he's found someone else, online or whatever, and is playing happy families back in his home country.
On the flip side, he's telling them that he has to stay working in the UK, for the sake of his children here, or because he can afford to send more money "home" but spends the longer holidays there because that's "their time" with him. Meanwhile they're all oblivious to the fact that he's living a full, married life in the UK with the mother of his children.
Is there a way you can search public records in his home country? Property, births, marriages, etc? I'd be looking him up anywhere I could.
I'd also be looking through everything at home, looking for any sort of paperwork he might have left in the UK - income, bank statements, anything. Not so easy nowadays with a lot of stuff coming electronically. Does he have a computer or the like that he might have saved login details on that you can get into? I have gone "paperless" at home and shred everything that comes in, but I save scanned copies to a OneDrive that my DH could access if he really needed to.
Something tells me he's going to have everything squirreled away where it's difficult to find though...