I suggest you tell your adult children about their Dad’s living arrangements, etc. I’d tell them even if they were not adult. If you do not, when they find out - then what? You do not need to hide this. Stick to the facts, be sincere and honest - just be yourself. Your kids deserve the truth.
I know you are considering the purpose in telling them. Also what is the purpose in not telling them.
As I said just a suggestion.
You’re waking a really fine path. Compassionate and understanding. You so got this.
DnJ
Feelings are fleeting. Be better, not bitter. Love the person, forgive the sin.