Rhodey looked from Sophie to Tony and back again. Somehow he got the feeling there was more going on here than what he was aware of, but he wasn't sure what. Sophie didn't look like she was trying to pull anything...
He looked back to Tony for a second, and then looked back at Sophie. "If your parents are cool with it, then yeah, I'll teach you how to fight." He definitely wasn't going to teach her if her parents didn't approve. While he did think that she should know how to defend herself, especially in a world where there were both good and bad super-people in abundance, he wasn't going to overstep his boundaries.
Publicly, and in front of her parents, that was his story. If this was something she reeeeeally wanted, and if she knew how to be quiet and subtle about it, then maybe he'd consider doing it on the sly. Mostly because of the aforementioned belief that she really should know at least a few self-defense techniques in a world like this one.