Attire at Catholic funeral in the South?

Factual Questions
1

My daughter and I are going to a funeral this evening (her ex-boyfriend’s mother) at a Catholic church. I haven’t been to a Catholic church in many years – like, back in the '70s! – but I remember having to wear a hat, or, since I didn’t have a hat, pin a hankie on my head. I’ve heard that this is no longer the case, but my Catholic connection is incommunicado and I want confirmation.

Also, I’ve only ever been to funerals in California, which is a good deal more casual than Virginia. In California, I’ve always just worn modest, quiet, church-type clothes to funerals without sweating that they be black. As it happens, I have a black coatdress with off-white collar and cuffs, but what about my daughter? She’s 16 and doesn’t have anything black that’s also appropriate for church. I was going to have her wear an olive green pants suit with a black shell underneath. Will that be OK?

2

I’m not American, but those clothes sound fine to me for a Catholic funeral.

3

Catholic in Tennessee here.

The clothes sound fine - the main thing is that they are subdued colors, so both outfits sound appropriate.
You have no need to wear a hair covering in a Catholic church anymore. No one will (or should) look at you strangely, ask you to cover your head or anything if the like.