Is it possible for the problems of the husband's friend's pregnancy to transfer to the questioner's pregnancy if her daughter wears clothes from the husband's friend's daughter?

What your mother mentioned about the dependency of children's death or survival on wearing these clothes has no basis in Islamic law; it is a matter of delusions and superstitions. There is no harm in using these clothes. Try to convince your mother of this matter, and if you cannot, then do not disobey her and maintain wisdom in your dealings with her, avoiding conflict. You can donate them to another child to avoid disagreement.