I think
Katherine is really nice. I like this spelling best but
Catherine is also nice.
I think
Katherine is common enough that it wouldn't matter if the cousin had the same name, especially since they rarely meet, especially if it's the middle name and especially if it's spelled differently. I don't think people would assume she was named after cousin
Catherine or anything like that.
Willow Katherine is my favourite of those three combos, it just flows nicely. I like the name
Caroline but
Caroline Katherine sounds strange to me - too many similar sounds and emphases in there.
my top
Katherine combos would be
Elsa Katherine,
Alice Katherine,
Maya Katherine and
Phoebe Katherine.