You didn't say why your d-i-l "hated" the baby quilt you made for her. I'm so sorry for that. Shame on her!
As for a floor quilt, I'd want it to have some body so it doesn't wad up as the baby moves about.
I don't know that I'd want fleece as the batting but it might work well simply putting it as a "combined" backing as well as the batting. it will be quite warm. If it's to be a throw, I like the self-binding little quilts that Jenny Doan first brought out the instructions. Those can end up as about any size, are light weight and drape quite well. No batting.
My personal choice is the light polyester batting.