I have a second cousin born in 2021 and died in 2020. Her son, husband and all siblings have also passed. The son's wife is still living. Do I need her permission to have this cousin's Temple Work done???
According to the guidelines in the knowledge article, "How do I request ordinances for an ancestor who was born in the last 110 years?" you must receive permission from a close living relative before you can reserve the name for temple work.
In the situation you describe, it does not appear that there are any close living relatives. That is, there is no undivorced spouse, an adult child, a parent, or a sibling.
If no close living relatives exist to grant permission, you can still request permission to do the ordinances. Please be prepared to provide evidence that no living close relatives exist.
Please review the knowledge article mentioned above for complete instructions: https://www.familysearch.org/help/helpcenter/article/how-do-i-request-ordinances-for-an-ancestor-who-was-born-in-the-last-110-years.