I also don’t see a problem with stepmother, since “mother” is a different word than “mom,” and only the latter has to be someone who took care of you.
But, if the OP doesn’t like it, I would suggest “[father’s] lovely wife.” That way you don’t have the connotations of not liking her (unless you make it sound sarcastic, of course). I mostly imagine an actual introduction being in the form “This is my dad ___ and his lovely wife ____.”
Outside of that, I’d just use her first name to talk about her. If people ask who she is, then maybe say “Oh, my dad’s wife. I didn’t grow up with her, but she’s pretty nice.” And then go on.
That said, I’ve not been in this situation, so I’m just imagining what sounds natural to me.
In my experience, the usual is for the person to be introduced as “my father’s wife”. “My stepmother” seems reserved for someone who actually acted in a parental role.
“Second wife” evokes images of “second-hand” or “sloppy seconds”, which you should avoid. Instead, it may be best to use the term “final wife”, but only if you are sure that she will be the one to see him into his grave. If not, use “sloppy wife” or “nowest wife”.
In a situation where first names are not appropriate, my step daughter refers to me as “My Mother’s husband”. I refer to her as, “My Wife’s daughter.” I called my stepfathers “My Mother’s nth Husband”, where n=1,2 or 3.
My Father died when I was 16, and it wasn’t easy to deal with her 2nd husband who insisted on calling me, “Son”. Otherwise he was a nice guy.
