As to Force Pushing -- I'd have to be shown how Anakin comes off as bullied or angry or anything but happy to be racing again. Giving him Force Pushes in the race diminishes his piloting ability -- someone good enough to win without Force Pushes is better than someone who lashes out and stuff.
We'd need to look for a place to do it -- like if he used the force instead of that magnet hammer to get his loose hose back or something. Using the Force to cheat in a race would turn Qui Gonn off; but maybe using the Force to fend off an attack so he can win fair and square might work. I mean, we're looking to see if this guy is the CHOSEN ONE, not just some gifted kid. It's like if we saw the Bhudda or Jesus using special powers to win at cards or something -- you'd just know in an instant: this guy may be powerful, but he ain't the Chosen One.