I have done this before though and the result was H breaking up with the OW and coming home to visit, he came home and spent some of his time here online dating (he is not aware that I know this). It also fed into his martyr syndrome - he had given up his OW for the sake of a wife he is not in love with and his children. He hurt the OW and felt bad about this but most likely this was my fault in his mind.
That was over a year ago. However, they got back together again for a while until she put pressure on him to make a decision - he still said that he doesn't want to hurt people he cares about (his wife and children) so she asked him not to contact her again. He agreed to this but checked up on her via a female work colleague who is a friend of hers. He is now in contact with her again and she is allowing it but as far as I know they are not together.
So, as it stands he is seems to be searching for another relationship with a woman who will accept his way of life, i.e. two worlds, his life at home here with his wife and children and his life in Moscow as a single man with no children and no ties. He has met several (some of them are very young, 20's / 30's), he meets them for lunch, breakfast, attends events with them, the cinema, exhibitions, it is not about sex but voyeurism comes into it, sexual innuendo, touching, whatever they will accept.
This seems to allow him to tell me that he is not in a relationship and therefore can come home.
I have no problem asking him not to come home if he is in a relationship but he will say that he is not - what do I say /do then?
In some respects it would be easier if he was with one woman, such as the original OW, in an acutual relationship as he was for the first year, that way I could set a boundary putting pressure on the OW to provide for all his needs and allow the A to come to a natural end. But, the way this is going seems impossible..............