I think you are right op, they need to hear it from you. Especially now your parents know, I know my parents would be incandescent and if they happened to be around my husband and the kids were there then my Mum would not hold back. Nor could I expect her to! That’s just who she is!
You are going to need family and friends around you to recover, the kids are going to feel awful if you stop talking every time they walk into the room, or they hear whispers and you won’t tell them what was said.
I would have preferred the truth, I have parents who even now twenty years on hide important things, apparently so I don’t get upset. It made me so angry at 16 and just as much now. Teens and young adults can handle more than we give them credit for.
I found that being lied to and the whispering and talking ceasing before I entered the room, made the actual thing worse. I couldn’t understand why they didn’t just tell me.
Unfortunately, the OP’s children are going to suffer no matter what, op’s husband chose that for them. It’s better that they have the truth, then OP can support them and get them counselling. Lying is never a good idea, skeletons have a habit of forcing there way out of closets!
In op’s shoes, I would say that I know they love their Dad very much and that whilst they are understandably hurting, he is still their Dad and you fully support their relationship with him. He may have failed as a husband but he loves them very much and you know that they love him. They are not to feel like they are betraying you by continuing their relationship with him or likewise.
I would also be careful not to run him down, putting emphasis on his actions/ behaviour rather than who he is as a person. I would also perhaps use the word escort instead of hooker/ prostitute. I am sending so much strength your way!