So now that Jemma has said that Kate is married to a woman here is my head cannon on how the show presents it. The Doctor will land the TARDIS in Kate’s home and just waltz into her room and tell her to get up for some kind of emergency. Kate will spring up (preferably without a shirt clutching her sheets) and then her wife will pop up (also holding up said sheets) asking who the strange man in their bedroom is. Poor Bill would be so confused with this being her first meeting of one of the most powerful women on the planet Earth.
I kinda picture the wife being played by Catherine Russell, but that is wishful thinking.
If they actually show any of Kate’s personal life we might finally find out the name of this mystery second child.
“I think it was a complete mystery about when we joined the Doctor and what they had done beforehand. I mean, in those days…its less of a mystery now because he has a place that he came from. In those days nobody knew where he came from. Nobody knew whether he should have been on the TARDIS. Nobody knew whether he’d stolen it, whether he’d simply started off many many years ago and had forgotten how to work half of it. How long had they been travelling? Who knows?” - Verity Lambert