Tanya, I completely understand the predicament you're in. My MIL and I are always trying to guess at what the other would like. For my birthday, she sent me a hot pink rock necklace and a matching bracelet. Definitely not my style. I told Brendan not to tell his mum that, but he did anyway when he was in England! >:( (I think she asked him the kind of stuff I like as gifts). I felt terrible. But he said that she didn't mind, and then he told her the sorts of things I do like. So, it turned out okay, but I still feel badly that he told her. Anyway, I've gotten loads of weird stuff from her when Brendan and I were first together. I had a hat like the leopard one you have, but it was fake suede/shearling instead. It was black, and had a pom pom on top that was made of the same thick material as the hat. I swear, it looked like dreadlocks. :D I just gave it to Goodwill a few days ago, and now I sort of wish I hadn't because it always made me laugh when I put it on (I never left the house though).
Anyway, long story short, I think the longer you and Pete are together, the better she'll get to know you, and the better she'll be able to tell what you like. I finally just asked my MIL point blank the kind of stuff she likes getting as gifts. It's hard when you can't spend a lot of time together in person, though.
So, I'd probably keep the fur scarf stashed somewhere, even though I'm against wearing actual fur. I love animal print--I'm not quite sure what to make of the hat and gloves. I'd probably stash those too, until you feel comfortable giving them away (the day will come when you feel like you know Pete's mum better, and she knows you).
I like the chunky grey beret hat and the slippers--so cute!