Does the sister's son become a foster brother to the questioner's children if he (the sister's son) drank a single sip of his (the questioner's) wife's milk unintentionally?

If the child did not suckle more than one dose, then he is not considered a brother to your children through suckling. The preponderant opinion is that the suckling which prohibits marriage is that which reaches five known sucklings within the two years [of infancy]. There is no difference in the establishment of prohibition whether it was by your choice or not by your choice.