I’ve never seen that spelling before (nor the other proposed spellings) so not really trendy but I also really don’t like it, to be honest. It seems like a drug (Ritalin) or a chemically generated carrot derivative to me. Carolyn, which I think is the prevalent spelling, is a variant of Caroline so you’re not mitigating the same source issue by switching the spelling up to Caralin.
You’re not beating the pronunciation issues with this spelling either. I’d rather just name/be named Cara (which for the record, I would say CAH-ruh, not CARE-uh or CAR-uh/CAAh-ruh).
Catherine is a better choice imo. Catherine with a C is a lot easier to say than Carolyn but C-a-r-a-l-i-n. I don’t know any young ones who are called Cathy; Cate/Katie are generally the go-tos if not the full name being used full time. And besides, you want to call her Carey anyway. I’d probably use an R middle name to solidify the nickname; Catherine Rhiannon or something like that.