Dandy is pretty weak physically.
It's not like he has bad stamina but it's more the fact that he isn't too strong. Almost all toons would be pretty much able to hold him to the ground in a fight, if it would ever happen (or if the toons would ever want to hurt him...). Dandy is aware of his weakness here. Luckily for him other toons don't seem to point it out, Dandy is actually happy that they don't do that.
He often gets dragged around by kids because he can't really stop it. Even if he tries to act he gives up after 10 seconds. Dandy never really liked it at all (it makes him uncorfortable and even scared), but he wanted to make kids happy, thats his job after all. The whole things of being dragged around by kids was big enought deal that Devan went to comolain to Arthur and Delilah about it. After that Dandy spends most time only in his shop.
Dandy always claims that he dosen't mind being jerked by kids, but after something like that happens he often gets all more aggresive any time other toons even try to touch him (Dandy isn't too aware of his behaviour change).
Maybe Dandy isn't the strongest one of the toons, but he surely is the most clever one. He dosen't shows it often thought...