Oh sweety big hugs for you. I hope that everything goes well with your sister. I know you'll be sending her lots of love. I know it's hard but try not to feel bad about having a healthy baby, because there is absolutely nothing wrong with that it is great news, it's just so sad to hear that your sister is going through this.
I'd be upset at your sis partner if I was you too, especially because your DH offered to help out to make him supporting your sis possible.
Best wishes for your sister, you and your family while going through this tough time.

Love