A mishna on Yevamot 97b says (Soncino translation):
The sons of a female proselyte who become proselytes together with her neither participate in chalitzah nor contract levirate marriage. Even if the one was not conceived in holiness but was born in holiness, and the other was both conceived and born in holiness. So also where the sons of a bondwoman were emancipated together with her.
The case of children who convert along with their mother seems clear to me; halachically speaking she is not their mother and so they are not brothers to each other, so yibbum doesn't apply. But I'm confused by the part that says that two brothers both born after their mother converted (one was conceived before too, and the other not) are also not obligated in yibbum. I was taught that a child born to a woman who has already converted is fully a Jew (modulo some minor exclusions with, e.g. marrying a kohein); those sons are not bnei Avraham Avinu but, rather, bnei (whoever her Jewish husband is).
The g'mara discusses this on 97 and 98 but I'm having trouble following it. It seems to involve comparison to the bondwoman mentioned at the end of the mishna. What are the mishna and g'mara saying here about children of a giyoret?