Is the son of the sister from her first husband considered a brother by suckling to the questioner's daughter, or is the prohibition of suckling limited to the children of her second husband?

The sister through fosterage is one of the mahrams, based on the Almighty's saying: "And your mothers who have suckled you, and your sisters through fosterage," and based on the Prophet's (peace be upon him) saying: "Indeed, fosterage prohibits what lineage prohibits." The prohibitive amount in fosterage is five sucklings. So, if your sister breastfeeds your daughter five times, the daughter becomes her daughter through fosterage and a sister to all her children, whether from the first or second husband. Consequently, she is a sister to your sister's son from her first husband.