Actually, when you marry, either spouse, you leave your parents and become one, so my answer is your wife regarding this question. Hard choice, but wife is the way to go unless mom really needs help and the wife agrees...
You shouldn't be forced to answer that question unless someone is being unreasonable. A wife should come first but under normal circumstances you shouldn't have to abandon mom. Mom should not get in the way and the wife must understand that mom is not going anywhere.
Mother! Unless you've been with your wife for more than 18 years which is the amount of time your mother had to put up with everything you dished out unconditionally. If your wife is making you disregard your mother and your mother is making you disregard your wife I say have nothing to do with either of them until they learn to share which I'm sure they learned when they were children. Good Luck!!!!
Usually wife, but if mother has a serious need for help due to a medical problem, or is recently widowed, or if her husband has problems & she needs help with him. It works the other way as well, where the husband should usually come first, unless his wife's parents seriously need her.