Cheating in a marriage is morally wrong! But if you wish to stay on. Lets look into a paradigm shift!
1. Every family needs to be financed, hence one party have to work.
2. Your husband works overseas, most likely is difficult for him to come back and given that he made the effort to fly back every alternate weekend shows some commitment on his end.
Maybe is time to look into why you can't move and see what is your priority.
If it is child education, I am sure you can find an equally good school there for your kids with the amount of money he is earning.
Forgotten to add, you have to file for divorce within 6 months of the discovery of adultery or they will assume you have lived with it.
Usually the court will order cost of application to the defendant if found to be true.
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