I completely understand, I was in a similar situation, but thankfully they got a flat. DSD was 20 and got pregnant, but really dragged their feet about finding a flat, neither were working. She lived with me and DH. At the time, me and DH were actively trying for a child, and the whole situation felt like a huge shock. I would not have been able to handle it if they hadn't found a flat. Imagine, we'd both be bringing up babies possibly in the one house!
And I did get pregnant soon after. DSD was very weird about it, I think for her it was all about her and the baby, would try to get us to babysit a lot when we had a much younger step child too to look after. But like you, I think the feeling of all the attention that a new baby brings when you are actively trying but having fertility issues is just too much.
No wonder you are having a hard time. I'd be finding flats for them myself, they've made a big adult decision and now both of them have to take that step and be adults. Keep the pressure up and also put down some ground rules when the baby is here. It's tough but I found with my DSD she'd not put any thought into the consequences, and being easy on her would have resulted in her just being more and more lazy about growing up. My DSD went back and forth to her Mums too, basically took the easy option and put off being responsible for herself. She's 20, not 16, it is reasonable to expect that she does not live with her parents now that she's had a child. If you want to support her, I'd put the energy into supporting her to become independent.
Eventually my DSD did learn to grow up, and she has started to take control over her own life and been a better parent for it. And I'm glad we didn't just let her stay with us as it would have completely broke us, DH would be alone, and it would have just delayed the inevitable for the DSD.
My DH did have a bit of shock and wondered whether it was a good idea, having another baby as a grandfather. Which was understandable. But don't let it hold you back from living your life. That your DSD has had a baby at 20 is her choice, so if the choice for you and your DP was to try for a baby then stick with that.