I can't speak for Dink, having never seen any Dink movie, but I really can't imagine Littlefoot to fight for being the top-dog (or rather top-dinosaur) of a group. While we accept Littlefoot as a kind of "leader" as most of the spotlight in the movies is on him, I'm not sure if Cera, Ducky, Petrie, and Spike (and Littlefoot too), would think of their friendship as hierarchicaly structured. Littlefoot does make many of the decisions for the group, but it is up to the others to decide whether to do what he suggests or not; Littlefoot is not ordering the others around against their will.
In LBT 6 he walks of by himself and the others follow only to save him from the trouble he got himself into.
In LBT 7 he is unquestionable the "speaker" of the decision to pursue the flyers, but Spike is the one who really goes ahead.
In LBT 8 we have Ducky and Spike acting rather independently from Littlefoot.
In LBT 9 he surely makes the decision to bring Mo back to big water leaving Cera, who was the only one who might have objected, no real chance to contradict.
The list goes on and there are many cases in which really Littlefoot decides what to do, but usually the others agree only if they feel like it, not just because Littlefoot wants them to.
The original movie provides the best examples for Littlefoot not desiring to pose himself above the others (Cera in particular). Rather than leaving Cera to the embarassment that she couldn't get food by himself he drops some leafes on her, making her think that it was her who shook the leaves down from a tree. The others followed him mainly because he knew the way to the Great Valley, and they stopped following him when they felt Cera's way was easier.
In LBT 2 we have Littlefoot tell Cera: "No one is making you come Cera!"
While the others often accept a kind of leadership role of Littlefoot I'm quite sure that Littlefoot wouldn't fight over it. The others either agree with him, or they don't and that is that. A friendship can be one of two friends on the same eye-level. I don't think Littlefoot wants to dominate others, not to mention use violence to achieve this.
