My kids are young, and while I would definitely want them to understand that we love babies and support mothers, I also would want them to understand that mommies having babies without daddies is NOT the way God intended it.
I’ve always been open about my conflicts of emotions with my kids. When my Grandmothers died, I told them I was happy they were going to be with Jesus, but sad because I was going to miss them. I couldn’t just tell them one part of the story because it wasn’t authentic, and they’d pick up on that. In the same way, I think it is appropriate to tell young children that we are happy that there is a new baby in the world, and that we want to do everything we can to help the mother and baby… but that we understand that God wants babies to be born to married couples. Maybe some kids wouldn’t get it, but some will, and I think it’s worth it.
So I’d probably wait as long as possible (after all, if there was a miscarriage, they wouldn’t need to be told at all), and then just explain that she is pregnant. I’d look for the opportunity to explain your conflicted emotions (see above). This way you are not confusing them into wondering if marriage really is supposed to be a precursor to children or not.
If the children ask how the mommy can get pregnant without a husband, then just say, that God makes babies WITH the help of the mommy and the daddy. This baby has a daddy too, he just isn’t married to the mommy. If they ask for more details, give them gradually and only if they are asking:
step one - you can mention the seed and the egg and that they have to combine.
step two - the man puts the seed into the woman
step three - a husband and a wife have a special kind of cuddle that allows this to happen.
However many details you give your child about the mechanics of reproduction, you can say that God gave men and women the ability to make babies, but he wants men and women to get married first, because…(insert practical and spiritual reasons here)… However, sometimes people act as though they’re married when they’re really not, and this is why they might end up having babies without being married. I would say, “I am very sad that Auntie made some bad choices and acted as though she was married when she wasn’t. But we love her and our little cousin in her belly very much. And so does God. And we can’t wait to meet our little cousin!”