How should I refer to her parents?

I'm going to be totally unhelpful and say it really depends on the specific scene/sentence. All three could work in certain situations (substituting "her" for "Karla's." I don't think I would ever think of my dad as "Elaine's dad." That feels POV breaky to me, although I can see how it could be used in more of a descriptive scene.) If you do some more interacting around the community, maybe crit some other work, and get your post count up to 50 you could put a snippet up in SYW people could see and be able to offer more specific suggestions.

The Share Your Work password is vista. You could pop over and critique something new in the Romance/ WF forum right now!

In mine my MC's grandfather is usually just "Grandfather". I kind of liked the stilted formality of it for my character, especially since it seems to fit her being foreign. But I'm not sure it makes sense for a Russian, since there barely exists a word for Grandfather in Russian; they almost invariable use the diminutive dedushka, for which the best translation seems to be Grampa or Granddad.

My book is limited third, switching back and forth between the two main characters. When it's focused on her, I refer to her mother as she does: "Mama." When it's his perspective, I use her first name.

I had the same issue. At some point, I introduced their names in a natural way like so:

"Laylah, get your spawn some tea," Nadir's father said. His mother (blabla made tea).
And:
Nadir's father shook his head, took off one shoe, and slapped him across the face with it. "How do you think this affects my reputation? Soon everyone will be mocking me, Ashraf Arazi can't keep his son in line!"

You know, things like that. And then I just vary it between "mother/father" and "Ashraf/Laylah".

In my WIP my two characters' grandfathers are a part of the story. When we are in her POV, she refers to her grandfather as Pop and his grandfather as Henry. When we are in his POV, he refers to his grandfather as Granddad and her grandfather as George(in narrative) or directly as Mr. Williams since he has known her grandfather since he was a child(Southern respect).

If you're in her point of view, you refer to her parents by whatever terms she uses for them—Mother and Father, Mom and Dad, Mommy and Daddy, etc.

If you're in someone else's point of view, you refer to them by whatever form that character would use, Mr. or Mrs. Jones, Sally and Harry, whatever.

It's the same way you would refer to any other character. An underling will refer to the boss as Mr. Jones while a partner will call him Harry.