I have made a new hair/hat mesh with a hat over hair.

I would like it to work so that the Sim does not flip out into a different plain hair to swim, sleep, or anything else. Just leave the hat/hair on at all times with all outfits.

Could someone point me in the direction of the right line in SimPE to do this, and what it should read?

use a normal hair as your base? One that doesn't change? Then put your new mesh into it? That's what I'd do. If the person has seasons then they can choose anyway for each individual setting if they want.

Otherwise, there's some specific tutorial(s) about hats and hair and how to make them show up in various modes over in bodyshop skinning.

Well now that is a good practical option that never even dawned on me.

I'll look up those tutorials over in skinning too, since its a good thing to have knowledge of in general.

Thank ya!