Ooo good luck!
what I can suggest though is setting expectations when you do end up having to party: "Hey guys, i have a newborn so I might have to bail unexpectedly. ". I know if someone mentioned that before a run starts I'd be willing to wait. Or possibly find a more "casual" FC that will understand that you may have to leave on short notice.
Contrary to the "OMG OPTIMAL OR KICK" mentality you might see on a lot of the forums, lots of people who play this game are cool and understanding.
Congrats on the Baby!!!!!