What is the ruling on keeping a grave on which the deceased's name, date of birth, date of death, and occupation are written, when the parents are displeased, and is one sinful for leaving the matter as it is?

Building upon graves is forbidden by Islamic law unless there is a necessity. The Prophet (peace and blessings be upon him) forbade it and commanded that elevated graves be leveled. If demolishing the structure would only result in your brother's wife's anger, this should not prevent you from implementing the Sharia ruling. The structure should be demolished, even if it is a mosque or a shelter for visitors, unless it is needed for fear of exhumation or destruction by flood.