Kid2 + mortgage has to be a priority, but ignore me, i have both the 2 kids and the mortgage and it hasn’t stopped me buying bikes!
If you’re itching to upgrade something, what is it you want to improve? if it’s comfort/position/stiffness, look at frames. (or get some nicer bars/seatpost, etc) If it’s speed/acceleration/weight look at wheels.
You can always save weight with groupset choices too.
Look for a Kinesis/Boardman/Planet x frameset, or something similar. there are some lovely frames on Ebay/classifieds here/Cycling weekly. You can even prolong the excitement of buying shiny bits by steadily upgrading brakes/cranks/STI’s, etc, etc… If you buy a new bike now, you’ll only want something shiny to hang on it in a few months.
Of course you could just clean it and put some new bar tape on!
Having a second kid who is now 4 months, I’d say those longer rides might be swapped for a few early morning/ late evening rides when the brood is asleep/occupied. i wouldn’t spend a whole load of money on a bike you don’t want to take out at 6am in the rain. the longer stuff will come back in time, but probably not in the short term…