Am I obligated to forgive my husband who has committed adultery repeatedly, especially since there are children involved and in a country where hudud punishments are not applied?

If the husband commits adultery, he has committed a grave sin and done wrong by disclosing it. He must sincerely repent, conceal his sin, and be careful not to fall into temptation again. If he repents and mends his ways, then that is good and fortunate. Otherwise, there is no benefit in remaining with him.