I just typed up essentially the same thing, then just tiredly deleted it all.The Chewie thing isn't even that big a deal.
1) He just tried to murder her son.
2) He's concerned with getting Finn medical attention.
3) She's looking right past him to Rey, anyway.
If they'd just pushed in on the shot a little bit more, you wouldn't have even seen Chewie on the edge of the frame as Leia looks at Rey, and a large number of these complaints probably wouldn't be lodged.
But yeah - Chewie's all about getting Finn patched up at that point. Also, Chewie doesn't seem to be the kind of character that's about hugging in those instances. When he thought Han was dead on Hoth, he didn't walk over to Leia and hug her, either. He howled at the sky and thunked his head on some metal thing or another. Emotionally distressed Chewie likes to be by himself, I guess.
Probably would have played better if Leia interacted with Chewie in some way as he walked by, or he wasn't kind of half in the shot and half out of it, or they made more of a point of Chewie rushing Finn inside with the medic people, but there you go. The first we see of him after this is him quietly grieving by himself inside before R2 boots up.
As for why Leia hugs Rey, it's because of the people who went down to the surface to get Rey, she's the only one left standing. Han is dead and Finn (who Leia personally thanked for defecting and saving Poe) is seriously wounded and in a coma. They both lost something and are having a shared moment of grief, in contrast to the celebration of the larger victory around them.
I'm finding it interesting how so many of the complaints in this thread are just really honing in on these weirdly specific things that are frankly kind of meaningless in the grand scheme of things, or even complaining about elements that are actually examples of strong filmmaking, while some of the more big picture things that are a bit sloppy are barely even touched on.