Rumer Willis — Rallying for Demi Moore at Hospital

Rumer WillisRumer 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 had hospital visitor”s passes on their jackets.

broke the story … Demi was rushed to the LA area hospital on Monday night. Demi”s people say she is staying at the hospital to seek “further professional assistance” to treat exhaustion and deal with substance abuse issues.