What should a young man do who wishes to marry a girl in whom he sees good, while his family (his mother and sisters) reject this marriage because of the girl's father smoking and having a slight disability, and her sister having Down syndrome, and their claims that they are not "like them" and their fear of having disabled children?

The Sharia encourages marrying a woman of religious commitment. If the girl in question is religious and of good character, then it does not matter that her father smokes and is disabled, or that her sister is disabled; this is not a legal impediment. Strive to convince your mother, and seek help from people of virtue. If your mother is not convinced, then the default is to obey her and not marry the girl, unless there is an overriding benefit that contradicts this. Upholding filial piety towards your mother may be a reason for a blessed marriage and good offspring. Do not pay attention to anxieties such as giving birth to a disabled child if you leave this girl.