Is the wife obligated to visit and stay with her husband's relatives whom she does not wish to visit due to their excessive backbiting and criticism? And is she sinful for refusing to do so? And is the husband entitled to be angry at her refusal?

You are not obligated to visit your husband's maternal uncle (khal) or paternal uncle ('amm), nor to stay overnight with them, and your husband has no right to force you to do so. However, it is advisable to visit them, as this is an act of kindness towards your husband and helps him maintain ties of kinship, which is a good deed for which you will be rewarded. If your husband's maternal uncle's wife engages in backbiting, you must gently and wisely forbid her from it, and it is not permissible for you to listen to backbiting. If you are unable to verbally object, then you must object in your heart and leave the gathering if possible. You can also initiate beneficial conversation to steer the discussion away from idle talk.