The pair is battling to keep their mother-daughter relationship on track, reported Radar online.
"Demi and Rumer have been working on repairing their relationship. But the problem is that Demi wants to go out and party with her again and that is where all the problems started before. They're apprehensive," a source said.
The 50-year-old actress had become estranged from Rumer and her other two daughters, Scout and Tallulah, in the wake of her split from ex-husband Ashton Kutcher and her subsequent stint in rehab.