@Cheated85, your H is indeed a disgusting pig. He felt entitled to defile your marriage, the family home, and your children’s school with his sleazy sexual affair. That he chose to humiliate you with a woman in your orbit was twisting the knife. He has made you the object of pity and gossip.
My advice is to take control, shine a light, and tackle this. Avoiding and sweeping will have pervasive, damaging consequences, and you would not be doing your children any favors. Would you want them to ignore and swallow infidelity/disloyalty in their future relationships?
H knew exactly what he was doing. He had quite the devious agenda, which rumbles his current clueless act. His disingenuousness makes him a poor risk for successful reconciliation. If you do stay with him, he needs to take full responsibility for restoring trust and helping you heal. This includes
(1) disclosing the full story (2) NC with OW with a break-up message in your presence (3) open access to devices and (4) digging deep in individual counseling to examine his weak character traits that led him to trash his family for cheap thrills and illicit ego validation.
In my view, the smart move is to employ a sharp shock by showing him the door while you process. He needs to feel the loss of you—to feel the ramifications of his cruel, unethical choices. Personally, I would make the separation permanent, but you may choose differently.
@Cheated85, you don’t yet have the whole story, so you need an STD test. (Swearing on the children’s lives is standard cheater-speak, as demonstrated by countless MN threads.) He could have rendezvoused with OW via lunch time, leaving work early, secret days off, errand running, etc.
Delete smug OW from your SM asap. Be icy cool and detached at the school run. I would inform her H. He has the right to know…just as you did. 