Josh being there in the delivery room would put a great distress on Casey, unless she wants him to be there with her! I know it is difficult for her right now with him walking out of her life and filing for the divorce, but later on she will be thanking God for getting him out of her life as a husband, but he will always be in the picture because of the baby he fathered! If he doesn't pay child support than he has no rights at all.
When Susan and Dan divorced they had Jennifer and he wouldn't pay child support, and owed thousands of $$$$ to her, so when she married Bill and he became her father with him adopting her, that Dan didn't have a say in it, because he either paid all the money he owed in back child support or leave her out of his life.....So he hasn't seen her in years! She is married now with three children of her own and a fourth on the way, I hear!
Just be there for Casey and help her when you can, but don't let her take advantage of you and Sherry by thinking she doesn't have to do anything and can stay there forever, as it wouldn't be right for her or you and Sherry, either!
It's difficult to say NO to your children and grandchildren, but sometimes for their sake, we must....just like God does, when He knows what we want would not be for our good nor His purpose!
Prayers for you all and may Casey have a healthy baby boy and give all of you lots of blessings! They are so precious in ours and God's sight!

God Bless! Betty