Is a mother entitled to be angry for not being taken to Hajj and for a wife being favored over her? And is a son sinful if he does not spend long hours with her as she desires, knowing that he strives to be just between her and his wife and children?

You should have taken your mother for Hajj because it carries a greater reward than taking your wife. However, since what has happened has happened, you should now try to appease your mother and promise her Hajj in the future if it becomes feasible. You are not sinful for not taking her for Hajj and instead taking your wife, but you have missed out on a greater reward. You must balance your relationship with your wife and your mother, and give each one their due right.