Is it permissible for the son of the second niece to marry the daughter of the questioner if the questioner has nursed her niece's daughter twice?

The suckling that establishes prohibition is five satisfying sucklings. Accordingly, if your sister's daughter only suckled from you twice, she is not considered your suckling daughter, nor is she a suckling sister to any of your children.

Your sister's son is not a mahram to your daughter, unless you suckle him, or your daughter suckles from his mother's milk or his father's wife's milk, or they both suckle from the milk of one woman or one man. A suckling brother is one who suckled with another from the milk of one woman or the milk of one man, or suckled from the mother of that other person or from his father's milk.