Vudu will work but you would need a Movies anywhere account, and under add retailers, add Vudu to it and also pay for a Amazon prime account to add to movies anywhere. Then you can download the movies from Amazon, under my stuff, purchases & rentals, movies tab,
rmcaw52
I know that.  I've done that since Disney Movies Anywhere became MoviesAnywhere, and used DVDFab DRM Remover for iTunes.   I have my MoviesAnywhere account linked with my Amazon, Vudu, FandangoNow, Comcast, Google Play, iTunes and even my cousin's Verizon FIOS account :D 
To be honest, with DRM Downloader and Amazon,  I get better picture and sound quality than the iTunes downloads, so I will rarely be using DRM Remover for iTunes movies anymore. 
I've asked for Vudu because unfortunately there are some purchased movies I have from the UltraViolet days that don't work with MoviesAnywhere.  Not to mention that a hand full of studios like Lions Gate and Paramount (and some others) don't participate in MA.  Vudu often runs some good $5 specials (which also happen to be non-MA titles).   All of that has left me with some of my purchases only existing in Vudu that don't sync to other services, and it would be nice to be able to get a local non-DRM copy of them as a backup, should they ever disappear from Vudu.