Unfortunately, whether or not he signs the contract is up to him. And there's nothing to stop him signing it and then walking out of his job and abandoning his responsibilities.
It will not look good, but really he's an adult and so can make any stupid decisions he likes.
Technically, in the eyes of the law you are now separated, pending divorce. There's nothing, now, that you can do about his decisions, I'm afraid. You are entering the 'living hell' stage of getting divorced where you watch them single-handedly destroy tons of financial benefits on to which you have a share, and on which you and your children depend.
If I were you, get your Occupation order/Non-Molestation and get him out if you can. From a pragmatic point of view, can you get a 'mortgage holiday' for a while? Have you spoken to the bank to see if you can get the mortgage repayments reduced at all, do they even know you have petitioned for divorce?
Your solicitor/you need to inform him that you have decided to proceed with the divorce and now wish to discuss the interim arrangements, e.g. how he is going to support the sinking ship, until the financial order and child arrangements are arranged. This is months and months of headache, but I promise you it ends...
You will just be very, very skint for a while I'm afraid. Same as the rest of us up and down the country, and he will start acting in a very spiteful manner. It's bloody hard (but worth it if you can get to the end).
KOKO.