Kate Stewart first appears in the direct-to-video Downtime, which makes it pretty clear that the Brigadier has not been the greatest of fathers. And yes, she is from a pre-Doris marriage that did not go well: http://tardis.wikia.com/wiki/Kate_Stewart According to The Shadows of Avalon, Doris is dead by the time of the novel (2012), in a boating accident. The last references to her being alive seem to be in Enemy of the Bane (2009) and Happy Endings (2010). There is a Short Trip, though, that hints that the Doctor may have altered that fate.
As a side note, Doris was scripted to appear in The Wedding of Sarah Jane Smith, until Nicholas Courtney's illness meant the script had to be rewritten to drop the Lethbridge-Stewarts.
^ Not getting the Brig into nuWho was a huge mistake. Almost unforgiveable. Should've made all efforts to do that while he was in better health. Mr Awe
Wait, that was the name of the story? Oh geeze. *facepalm* Yeah, nuWho made it abundantly clear that they'll try to use as much of the classic series as possible, which is fine. But I strongly suspect that they missed out on their chance simply because they just kind of took Courtney for granted. "We'll do it next year. We'll do it next year." etc. etc. And then boom, he's gone.
BRIGADIER: I'm getting too old for this sort of thing. He's all yours from now on. I'm going home to Doris. DOCTOR: Doris? BRIGADIER: Yes, my wife. DOCTOR: Ha, ha, ha. So she caught you in the end. It's funny you say that, since in a sense she did come out of nowhere. Unless the new series gave Marc Platt royalty payments as writer of Downtime - she was never a BBC character. So she appears to exist in a grey copyright area. Tennant met the Brig, the Tenth Doctor didn't. David played an army rival of the Brig's in the Unbound (non cannon) Doctor Who audio - Sympathy For The Devil. David even went to Nick's funeral.
Not only that, but we lost the Brig and K9. DWM printed some of the unused script, and it's basically a nice rehash of the Sarah/Rose jealousy in School Reunion. Quotes from memory, not check-up... Brig: Knowing what the Doctor thinks about computers, I can't understand why he'd see the point in a robot dog... K9: Analysing records, confirming results. Knowing the Doctor-Master's opinion of the military, I cannot understand why he would see the point of you. Brig: Touche. Of course, they then bond, so at the end the Brig leans across to the Doctor and asks if he's got a spare K-9 that he could have...