I don't think so. I'd say your aunt is "trendig", and a thing could also be "moderiktig".
I tried that, too, because of the other example that said "Rött är modernt i år," which they translated as "Red is fashionable this year." The thing is, people would understand what you mean with rött är modernt, but it is sort of a strange way to say it.
What Zmrzlina said, or what I often use: min ingifta faster, literally my aunt-in-law.
Nope, svär- indicates it's not your side of the family, but your spouse's.
No one would ever use it, but if you said "min svärfaster", everyone would (after a bit of confusion) understand it to mean your partner's father's sister or your partner's father's brother's wife.
I read it wrong the first time around and though it was "My father is a modern woman".