Hi Mummyalone!
As you've accepted the marriage is over, you need to get yourself sorted as soon as possible.
Go to see a solicitor and get the finances worked out - How much is your Ex going to pay for the kids / you etc., That will give you some clarity and security going forward.
As for the kids meeting OW... This is what we did:
I met with my DH's ex first (just the two of us) to talk about discipline etc., for the kids. Then we all met (Ex coming and going with the children, DH and I coming and going together - hope that makes sense).. Did this 3 times, to show the kids that DH and I were together and that the kids were with his EX (Established her as the resident parent, if you will and also that she was 'happy' with DH and me)
Then, eventually, the kids came to us.
The whole process took over a year and, in the time, DH saw the kids without me. I think that if you were to suggest such a plan, you would get a court to agree it as reasonable.... He shouldn't be considering having the kids meet a new partner until he established it's a long term relationship.
Also, think it's important that, in the short term, you ask for your Ex to see the children (without OW) for 1 day every weekend rather than a full weekend EOW (Every other weekend). That's what we did and, while it's tough, I think it's best for the kids - they are little and a fortnight is too long a time.... And he should be doing the driving. They are already having to cope with a new situation (The split), without having to contend with new homes / surroundings / people.
FWIW, DH and I have been together for 10 years and we have excellent relationships with the kids - It can work out OK. (The kids were younger than yours when the split happened)
Just concentrate right now on securing a financially secure future for your children.
And, you are always welcome on the step parent boards!