In the sentence who is saying "that's your business,isn't it ,cousin"
Laila remembered another fight, and, that time, Mammy had stood over Babi and said in a mincing way,That's your business, isn't it, cousin? To make nothing your business. Even your own sons going to war. Howl pleaded with you. Bui you buried your nose in those cursed books and let our sons go like they were a pair of haramis.
Solution 1:
I just Googled the first phrase and found it here, where it's clear (because it's in italics) that all of it after 'a mincing way' is spoken by Mammy. Laila is remembering Mammy saying it.