When I first read that Remus wanted to go with Harry, I thought it was odd, but understandable. With James, Sirius and Dumbledore all now gone, Remus would feel a bit responsible for Harry's safety. And he would justify his leaving his family by thinking they are safer without him. This makes sense since Remus has seen the people he cares most about killed. What would have been OOC is if Harry had said yes, and they'd had a party and Ron had shown up in a toga.
I had a happy moment when I thought: YES! GO! Because, well, I just wanted to see/read more about Remus. As the conversation progressed, it became obvious why he wanted to go, and why Harry wouldn't exactly agree with his reasoning.
I've also seen people suggest that the almost bubbly Remus that shows up to announce the news of Teddy's birth is OOC too. This is, again, the result of people not understanding Remus, I think, or simple underestimating him. I know we've seen this image of his as a rather serious character, but he is perfectly capable of expressing happiness. He was also a Marauder. I don't buy the whole he just planned while Sirius and James did everything image fandom seems to give him.