I watched The Land Before Time 2 with Mary, recently. The movie catches a lot of flak for being awful, and being a Disney-style ripoff of the original film. I agree that it doesn't have the same emotional impact as "young children dealing with the death of their parents". Still, I think it's pretty good. The characters are the same, the pacing is improved, and it has more story. When I rewatched the first movie, I was surprised at how many of the scenes have little to no dialogue, whatsoever. In contrast, the second movie has dialogue in pretty much every scene.
The story is that the children are feeling angry, because the adults treat them like little kids. They find and start to raise a baby on their own, when they realize they're being just as overprotective as their parents. There's also a minor racial undertone to the story, since all the characters are different species. They learn to overcome their differences, for the good of the group.
I'm guessing the villains are the least popular part of the film. The villains are two egg-eaters, who act and sound like Pinky and the Brain. They were rather goofy, and I think they were Mary's favorite part of the movie. Myself, I'm just trying to get the villains' egg song out of my mind.
The musical cues in the movie are pretty good. I didn't notice it as a kid, but some of them are taken directly from the original movie. We have the scary music, the sad/emotional music, and the music that plays when Cera and Littlefoot are arguing, and they're only two steps away from hitting each other. I have no idea why I remember that last, oddly specific, piece of music, but I did.
Overall, I'd say the movie is okay. A bit of a stylistic change from the first movie, but not the worst ever. If it had been super-awful, I expect the series would have ended here.