Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...
Asking you to forget about it is telltale that he feels entitled to do what he's doing, and does not respect you or your wishes. It can also signify that he's been doing it for awhile, since he was so effin bold to skip out once you'd gone with the kids, and think you'd believe the old fell-asleep-in-the-truck-at-the-bar bullshit story, then come home at 4:30 a.m. and shower? Give me a break!
If you let this go, you're courting grief, as he will just recommit once the coast is clear, without being accountable for his infidelity, his lies and deceit, and any repercussions going forward.
How did he meet this lady? Is he on a sex chatting platform, and if so, how long has he been on? If he has been, ask for the passwords so you can go to his profile and see for yourself when he opened the account, as well as all his other activities and pick-ups. Cheaters lie, and will continue to do so until you press for the truth. Now is your chance to get to the bottom of this and to strike while the iron is hot.
I wish you well.