Emily, you don't need to tell her to stay home with Daddy, she has already told you that she would.
When you leave, Wish her a Happy Thanksgiving and tell her to say hello to granma and granpa for you and tell her to have a good time. If it were me, I wouldn't even mention "daddy" specifically. Maybe you can buy her a centerpiece to give to her grandparents for their table on Thanksgiving Day. Or better yet, maybe she can make a special one.
Is pawn too strong a word? Perhaps. To me it "feels" as if this little girl is the prize in a tug of war between you and your husband, someplace no child should even be put in by anyone.