Is the husband entitled to prevent his wife from staying at her family's home in the summer, and from entering her sisters' homes, knowing that there are strange men (her sisters' husbands) constantly present, which causes him distress, and his wife is aware of this?

The sister's husband is a ghareeb (non-mahram), and it is not permissible for him to look at or be in seclusion with her. If the wife's going to her parents' house or her sister's house entails a forbidden act, then the husband must prevent her. If it does not entail a forbidden act, then he may prevent her, and she must obey him, but it is better for him to allow her for the sake of maintaining kinship ties. What the wife's brother said, that a man entering upon his wife's sisters is a matter of taste, is incorrect; rather, it is a clear legal matter. The sister's husband is not a mahram by consensus, and the noble Hadith warns against a man entering upon women and describes the hamu (who is a relative of the husband) as "death."