Rumer Willis — Rallying for Demi Moore at Hospital January 25, 2012 - by Celebrity News Wire Rumer Willis paced and smoked a cigarette outside the hospital where her mom, Demi Moore, was taken for substance abuse treatment.Rumer was visibly distraught and concerned Tuesday afternoon … as she spoke on the phone. Rumer and a nearby friend… TMZ Rumer Willis — Rallying for Demi Moore at Hospital