Does my sister-in-law have the obligation to support her mother-in-law

First of all, although your brother died and didn't divorce, their relationship between husband and wife ended naturally in law. Since your brother died, your sister-in-law has become a legal stranger with you. Half of your brother's money goes to your sister-in-law and half to your brother. Your brother's share of the money has become an inheritance, shared by your brother's children, wife and parents, which can be regarded as a part of the guarantee for the future life of the elderly.

Then he said, legally, even if your brother is still alive, your sister-in-law has no obligation to support your mother-in-law

China's Law on the Protection of the Rights and Interests of the Elderly clearly stipulates: "Supporters refer to the children of the elderly and other people who have the obligation to support according to law. The spouse of the supporter shall assist the supporter in fulfilling his maintenance obligations. "

Note that this is about assistance, not the obligation of spouses to support each other's parents.

Since your husband is still alive, he has the obligation to support his parents, and you have the obligation to help him, but your sister-in-law has nothing to do with your family and your mother-in-law. Of course, she has no obligation to participate in support and care.