I agree that Mama Rose is hands down the most demanding role in musical theatre.
I agree with many others said, but I'll also add Christine in Phantom. She's on stage for almost the whole show, and is still usually overshadowed by the Phantom. It's really up to her to carry the show.
And since the subject says "hardest" I'm gonna take that to mean something aside from most demanding--for instance Tony in West Side Story...well, it isn't a walk through the park...some of those high notes...damn. But also having to win the audience over is very hard for this character...when the Jets and Sharks get these amazing show off numbers like Cool and America, and even Maria comes to life at the end...it's really hard to be a standout Tony.
I guess some people could say similar things about Bobby in Company.
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli