Why can't I re-install YouTube? Error message: "Duplicate provider authority"
I had the very same issue except for the reason that YouTube got messed up.

I recovered using Root Explorer (installed from Google Play) on my rooted phone.

I used the search function to look for youtube (search is case insensitive) and it came back with five files.  I used multi-select and deleted them all.  I rebooted the phone just in case and then I was able to install YouTube with no more errors.