I second what oldwoman says. I can't imagine OW wanting a reminder of you in her life too often, it will be an imposition on their 'coupley romance' when poo-ey nappies and incessant crying come into it. We all know that our DCs are the most loveable and charming little people on the planet, but someone elses's - not so much!
Imagine this, XH wants to come and meet his brand new baby for the first time. How amazing will that be for him - she is not invited. A few days later he pops in again to spend time with DS1 and sees how much DS2 has changed in his absence. You get a chance to go and have a bath in peace and spend half an hour on yourself without being at the beck and call of a new baby. OW still has not met baby.
This goes on for several weeks - she will not be feeling full of joy about this baby, she will be pissed off that he is taking X's attention away from her and probably changing him into a pathetic, remorseful, guilt-ridden sap. You will get a few hours a week where you can legitimately step away from your beautiful DSs for just a short while, to recharge and come back to them re-energised and calm.
But as others have said, having a cry is totally ok. You have a lot changing in your life and things are not going to be how you imagined when DS2 was conceived. They will be better, because you will not be bringing him up in a relationship with a selfish man-child, you will be a capable and caring mum (as well as a kick-ass independent woman!) with XH there in the background for your DSs. He doesn't need to have any more influence on your life than that.
Hope you can regain your strength and start seeing your future life for the fabulous adventure it is going to be. x