In this passage, it refers to Roseann and her mother going shopping together in preparation for Roseann's babies arriving. You can tell this because the previous sentence refers to her family (and Joe's) being involved in the preparations. If it meant Roseann and her daughter (an older sister to the babies), the daughter would need to be mentioned somewhere in close proximity.
Mother-daughter can be used to describe other activites than a trip. It is not an everyday expression, but it's fairly common. To my ears it sounds more American than British, but I think that's because I would tend to say "window shopping with her mum" or something similar instead.