Rhodey had to hide his laugh behind a hand, pretending to scratch his nose. Oh yes, she was perfect for Tony. Of course the snark wasn't the only thing that made him say that... "What's all this 'James' stuff?" He grinned as he shook her hand. "I don't usually tell people I just met that they can call me Rhodey, but the way I see it, my best friend is happier than I can remember seeing him and you're a big part of it. That alone means you get to call me Rhodey."
He could understand why Pepper wouldn't want to talk to this Tony, but seeing this, seeing how happy he was...Rhodey couldn't bring himself to think badly of the situation. Ultimately what mattered to him was that his best friend was happy, and if he was? Then it was all good.
He extended the index finger of his right hand and lowered it to see if the little guy would grab it. "Hey there Edward. I'm your daddy's friend Rhodey." Later on, Rhodey would probably tease Tony about the image of him changing diapers, but right now Rhodey felt like there was sort of a moment going on, and he wasn't going to ruin it just yet.