Oomis, it seems that poskim are meikil when it comes to kids and tricycles (but not bikes).
I think baseball should be assur because of, as you say, uvdin d’chol, and, as I alluded to, and other posters mentioned as well, there is an issur to do things which require a straight floor, lest one fill in holes or flatten bumps.
The status of a car or truck seems to be kli shem’lachto l’issur, so it’s muttar l’tzorech gufo. Maybe climbing on it, even if it moves it a bit, would be considered tzorech gufo.