I agree you need to finish that conversation with H. And I like peacetoday’s suggestion of having the conversation away from the house.
Have you spoken with a lawyer?
How much do your kids know about what is going on? Or do you think they know? Kids are a lot more perceptive than we give them credit for.
D14, D12, and S10 will have questions. You are their support. You are the strong stable parent. Talk to them, let them ask questions, and answer them truthfully (age appropriate of course). They have a path to walk as well; their lives are changing too. Be their beacon. Keep shinning.
DnJ
Feelings are fleeting. Be better, not bitter. Love the person, forgive the sin.