Is it permissible for me to marry the daughter of a relative of ours who was nursed by my mother less than five times, and what is the ruling of Islamic law if my mother is unsure of the number of nursings?

If your mother breastfed the woman in question fewer than five times, then no prohibition of marriage is established between you and her, and this does not prevent your marriage to her daughter.

The suckling that establishes a prohibition of marriage is five feedings or more, and within the first two years of the child's life.

The fact that your older brother was nursed by someone other than your mother does not prohibit you from marrying the aforementioned girl.