Can my sister come to America with my mother on my mother’s visa?

No. You must separately petition your sister, who once approved by USCIS must still await the quota for a fourth preference family based visa. This quota is extremely oversubscribed, so it usually takes many years for consular processing. This often creates challenges for parents who will not abandon their children. A competent immigration attorney should ask the petitioning U. S. Citizen Child about whether their parent has children under 21. This often discourages immigration, so a few may avoid, neglect, or overlook the issue. I hope that your mom makes the right decision. Your sister will depend upon it!