So the मेरे being in plural is because of the बेटे, not the भाई? That seems a bit confusing to me... Also, what does bhai-on mean? I thought bhai was the same in singular and plural?
भाई is the same in both singular and plural in the nominative/direct case. However, in this sentence, के requires it to be in the oblique case, in which भाई is singular, but भाइयों is plural.
मेरे is oblique (not plural) because of the के, not because of the भाई. के is a postposition, and generally everything touched by a postposition has to go oblique.