So he won't stop paying rent (unless he does). Does his business have a physical presence in the city you are in now -- ie rented office space, etc or is it run virtually. If virtual, he can work anywhere right? What is to stop him from deciding to move in with the OW?
I realize I am pretty harsh, but I think you are very vulnerable. And once you are overseas, he holds all the power because he is here and you are not. I know you can't imagine him doing X or Y, but you are doing nothing to protect yourself.
What if he decides to seek a change in the parenting plan here, while you are there. You need so much documentation to make sure it is clear that he gives you permission to move overseas. I also think you ought to have geographic freedom to move whereever, but you need an attorney to write up those agreements.
And this OW or another woman could easily convince to behave differently. Please think of the worse case scenarios and do what you can to protect yourself.
At a minimum, you ought to consult with at attorney before you sign anything.