Unfortunately, the parade hasn't been "nightly" for a couple years now. For the past two or three years, it's only been on Saturday nights, followed by the concert. Any other day of the week (even Mardi Gras itself as far as I remember), you'll just see decorations and a couple empty food booths on a fake NY street rechristened the "French Quarter"--no parade.
Pat O'Briens has a branch in CityWalk that does a big party Mardi Gras night, if you're looking for something that Tuesday. Not kid-friendly, tho, 21 and up only.