Whatever choice you make I really don't agree that him not being able to be in the same country as his children should even be a choice.
You met in the UK, you married and lived together in the UK, and you had two children together when there.
So whatever has happened between the two of you, unless a parent is actually abusive or dangerous to the children, I don't believe either parent should be able to just take the children and leave the country.
He has offered to move his life himself to your country, and obviously you shouldn't have to live together when it makes you feel as it does, but there isn't really much more he can do to see his children than follow you if you've taken them away from him.
He seems to be a good father, whatever sort of husband he was, if he cares about his children enough that he's followed you 18 hours across the globe and said he will move to your home country (when he already left his own and made a life with you in another).
The people who say you should stay in your home country with the children and tell him to leave would not say that, I don't believe, if you were a father saying "I brought the children to my home country from the UK and now their mum's come here and is offering to live with us and stay here but it's making me depressed having her in the house. Should I tell her to go, and stay here with the children just us?".
People would be so angry and say it was parental abduction.... and you don't say what he said about you moving home when you left the UK for us to know whether he said that was ok with him, but now he's saying it's not, and has followed you there, or whether you just went because you wanted to.
But the most important thing here is the children, and unfortunately when you have two children with someone and make a commitment to their health and stability together, you shouldn't then make a parenting choice that affects them by yourself. Even if it is for your own "health" because, as depressed as you would feel living with him for two years, it isn't going to be as bad as a parent losing contact and parenting rights of their children because they've been taken 18 hours away. The the damage it will do to the children could be even worse. So whatever you do about living with him to get him into your country, or going back to the UK, you need to do it jointly with him and remember that, if you wouldn't be ok with him doing to you what you are thinking you could do to him, then it just isn't fair on him as an equal parent with equal rights as you to his children, and it 100 % isn't fair on them.