Complex sentence: They all turn to Liz to get rid of the dog, at first she refuses, but when they tell her she is a mother figure to them she finds comfort in the title and distracts the dog so that the staff can exit her apartment unharmed.
Split into simpler sentences: They all turn to Liz to get rid of the dog, which she at first refuses. Liz distracts the dog so that the staff can exit her apartment unharmed.