Her mum came across as controlling and not very nice even before the Doctor showed up though...
Not to me. Watching "Smith and Jones" the other day whilst introducing
Doctor Who to a friend, what struck me was that while Martha seemed to have a good relationship with her mum and dad, both of them seemed to be in their own little world because of their relationship problems with each other.
Martha was trying to play the mediator when she had to, and trying to stay away from it the rest of the time, and for the most part the situation was played for laughs. But "Smith and Jones" made it very clear early on that Francine was a woman whose husband had just left her for an immature twenty-something blonde sex kitten and was therefore understandably not at her best -- yet she was still trying to hold the family together and keep it functional.
I don't think Francine was a bad mother, or even had a particularly bad relationship with Martha. I think she was at a bad point in her life, and when the Doctor showed up, she sensed that he was potentially dangerous -- and then ended up misdirecting a lot of her anger at Clive to the Doctor, which Mister Saxon then exploited. I think it's very telling that at the end of "Last of the Time Lords," Francine and Clive are back together and Francine is embracing the Doctor, having realized both what a good person he is -- and that she has forgiven her husband. And when she reappears in "The Stolen Earth"/"Journey's End," her role is simply that of a loving mother.
I think, in other words, that Francine is probably someone who normally had good, healthy relationships, who we met at a really bad point in her life when she wasn't at her best.
ETA:
Honestly, of the three, the only Companion Mum who strikes me as being controlling and not very nice would be Sylvia Noble. She is, after all, the only Companion Mum who ever emotionally abandoned her child. "To be honest, I've given up on you..." "I was always a disappointment to you, wasn't I?" "Yeah."