The kids have gotten around to putting it on again. If still interested in talking about it, what domains are you seeing George and the Man in the Yellow Hat (MITYH from here on out) in?
I'd say the OS was maybe something about preparing for Christmas (The whole town sings "Are you ready for Christmas Day to come?" within the first couple of minutes. I forget the kids name, but that one kid is selling Christmas trees that get knocked down, the other kid is trying to write a Christmas song).
MITYH is trying to figure out what George's list means. He feels like he should know because he's supposed to know George better than anyone and being unable to figure it out is causing him problems.
George is trying to figure out the perfect gift for MITYH. The story plays like George doesn't know what to get him, but he actually has several ideas. He is either unable to create the gift (because he's a monkey and doesn't understand how things work) or they end up being things that MITYH doesn't really want in the apartment (the snow shaker thing). BUT I don't know that those things have anything to do with his influence on MITYH. I'm thinking that's maybe part of the "preparing for Christmas" throughline. George's influence comes from...being MITYH's pet, or best friend? Hard to say, really.
I don't really see anything pushing or pulling the relationship. They're best friends and nothing really gets in the way of that that I could tell. If there's any relationship, it seems to be in the scene where George is showing MITYH all the pictures he drew of their memories from throughout the story.
The best I can make out, it's a series of OS tales strung together by MITYH's tale running throughout. MITYH isn't even influenced to change or remain steadfast. He just kind of stumbles around until he finds the answer in a dream.