Tim following Grant around was supposed to be annoying, for Grant at least. You're seriously going to hate a 10 year old because he's excited to spend the weekend with his hero and is too young to understand that Grant wants nothing to do with him? Not to mention those scenes were important for Grant's character growth. As for the kids instigating the Rex attack I disagree. The Rex had already killed one of them and was on the hunt for the rest - the attack had already started. Yes, Lex shining the light got his attention, and was a "dumb move", but I looked at is as a computer geek recalling that fire scares animals away and the flash light, in her mind, was the closest thing to replicating that. Dumb move sure, but there was logic to it.
In any case, the kids in JP1 were the absolutely LEAST annoying characters in the franchise, and most movies in general. Honestly, the only other movie I can think of that featured kids who I enjoyed was Goonies.