Every time something terrible happens (to anyone) there is likely to be someone who takes pleasure from it. Those people often predict disasters accurately, because they only ever predict disaster, it's their only response to anything, so every so often they turn out to be right. They don't know anything special about the people around them, they just enjoy misery, the thought of future misery and they get pleasure from spoiling the special moments in life for other people.
My mother also did this to me, and for the longest time I believed that all her troubles (which were mostly invented!) were my fault. OP, your mother mustn't be allowed to get away with teaching you that men leaving are your fault. You didn't make this happen, just like you didn't make your father leave.
If it was so hard for your ex to live in this country, he could have tried to convince you to move, he could have worked out ways for you not to be disadvantaged by the move, or he could have worked with you to make it better for him here. At no point did you force him into bed with another woman. Counselling would have been reasonable and sensible. He could even have broken up with you, established a contact schedule with your children and then moved on, moved away and fucked whoever he wanted to. He could have thought of your joint children at any point, but he chose not to.
Adultery is never a sensible, kind or reasonable response to any problem. Similarly, if he choses not to keep in contact with his children (given how easy it is, with Zoom, Skype, email, texting,etc) then it would likely have made no difference. When he cheated, he would have abandoned every part of your life together, including your children. And he would have cheated wherever you were. There is no country which makes adulterers out of good men.
Please, whatever else you do, don't let your children think that this is in any way your fault. It will damage them, and your relationship with them.