Is your XM coming through the car's HU or through an all-access subscription running off your phone?
I have an XM subscription on the car's head unit, and it works fine with Android Auto working from my phone, and worked fine with my son's iPhone connected and CarPlay being activated.
But if your XM source is coming from your phone (rather than the HU) because, for example, you run XM from your all access subscription from your phone rather than the HU, that mat be an issue (and may be an issue that is easily solvable).
EDIT: Is your wife's phone plugged into a USB port, or is it connected by Bluetooth? Is your phone actively connected via Bluetooth while your wife is driving and her phone connected (via Bluetooth or USB)? Need details on the connections.