In my case, i was having daily snuggles with Lily until one day it said 'there is a small chance of her being pregnant' instead of 'something is preventing her from becoming pregnant'. Not really sure i did anything different, to be honest.
Anyway, that opened the floodgates. After that it was one shot one kid with anyone i had sex with which was... interesting.
So yeah, definitely hit a trigger somewhere, but i wouldn't be able to tell where that was. It may indeed be related to buying the farm (small pregnancy chance) and Daycare (normal pregnancy chance), but i can't be sure since it was a while back, though after knocking up Lily i did prioritize building the Daycare.