Mellie is fighting for Mellie. She married/wants to stay married for personal gain and not for love. She shows no real love for the baby unless it's a photo op. Remember that she said she would dance on Fitz's grave? She is not nice or hugable.
This is why I say the first couple deserve each other. I think they are both creeps.
What Fitz did with Verna was wrong and absolutely illegal ... but I wondered if perhaps Verna was seeking an assisted suicide to keep her "legacy" intact. Why else would she say everything she said to him?