With the remake its a problem with the Frame Rate. Higher Frame Rates can cause problems with the physics.

I am currently stuck on a level where an NPC puppy, that you have to guide, gets stuck due to this.

Stuck on it as we speak

Yup.
"You could have found an easier spot to get stuck!"

Compared to making the Supercharge Jumps in the original PS1 version, getting to all those hard to reach places in Tree Tops is frustrating if you aren't keeping track of how to do so.

we can all agreed that beating treetops makes us cry

Poor Spyro.