Does the wife's maternal aunt, who breastfed her, become the wife's mother through suckling, and thus become an unmarriageable kin for the husband? And does the ruling on prohibition through suckling differ between what was prohibited by lineage and what was prohibited by affinity, such as the wife's mother?

Your wife's maternal aunt (khālah) whom you breastfed is considered her mother through rada'ah (wet-nursing), and therefore, she is unlawful for you (muharramah). This is based on the Almighty's saying: "And mothers of your wives," and the Prophet's (peace be upon him) saying: "What is unlawful by lineage is also unlawful by rada'ah." The unlawful women by lineage and by rada'ah are similar; thus, the seven categories of women unlawful by lineage are likewise unlawful by rada'ah. As for those unlawful through affinity (musaharah), there are four who are permanently unlawful: the father's wife, the son's wife, and the wife's mother. These become unlawful immediately upon the marriage contract (whether by lineage or rada'ah). However, the wife's daughter does not become unlawful unless the husband has consummated the marriage. If the husband has not consummated the marriage with the woman and divorces her or she dies, he is permitted to marry her daughter.