If he had forgiven you sa pagkasala mo at first then cheated to get even sa ginawa mo, di na yan justified.
He forgave you sa una, so tapos na yung issue na yun. If di naman sa kanya okay kasi he can't trust you again then he should've filed for legal separation kasi di naman siya ground for annulment, kaya kasal pa rin kayo and mananatiling kabit yung pinalit niya sa'yo (somehow, panalo ka pa rin sa part na yan).
What you can possibly do is file a case of concubinge against them (I don't think if puwede siya magretaliate using your previous mistake kasi pinatawad naman niya and he didn't filed a case of adultery against you sa una pa lang) , depende na sa'yo if gusto mo ng legal separation tho it may be a better choice for you and your kids kaysa lumaki silang witness sa loveless marriage ni yo or sa pagche-cheat ng isa. Even if you fall out of love sa partner mo, you may still fall in love again after their past mistake kasi choice mo yun. And he chose the other woman over you ngayon, so there's no reason for you to really fight for your marriage kung ayaw na niya.
Instead, let him show during while separated na you really have changed na talaga for the sake of your family. Let them not watch your desperation to fix your marriage, bigay mo gusto niya through legal separation after mo mag-file ng case. Anyway, kahit mahal niya ng bongga the other girl, kabit pa rin si girl and they'll never be able to marry kasi kasal pa rin kayo sa batas.
Then, if gusto niyo na magbalik ulit, puwede naman kasi legal separation does not affect your marital status. Kasal pa rin kayo sa batas.
And, if below 7 ang kids, custody mo sila. If not, then you may file for the custody of your kids na mapunta sa'yo kasi this time ikaw ang innocent spouse.
*Make sure lang na you have the evidences of his sexual infidelity, para win ka talaga.
PS. I don't condone your past mistake pero I don't justify other partner's cheating just because nag-cheat ang una. Dapat hiwalay na kayo sa una pa lang, hindi yung maghihigantihan kayo. Psychological abuse sa mga anak niyo ang actions niyo.
Magbasa pa