I don't know that you have to tell him, but if you do, tell him its a temp job for 2 months. It will give you a chance to save up some for becoming independent.
I laughed out loud when I read about the Victoria's Secret being not so secret - I think it was awesome! Way to make him see you moving on!
You know, I don't think there is a judge in the world who would expect you to live in the house with H coming and going as he liked when he left you for another woman, and that the offer is only good as long as you are single. That's just so unreasonable, and I don't think any judge would let H attach those conditions to the offer.
I understand what the L is saying about turning down the offer looks bad for the kids, but you should be able to change the locks and H will have to stick to a schedule and take the children with him somewhere else to visit, and you should be free to see who you want in your home.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17