Chances are your Mother is good to go (with qualifiers)
If the iPhone is nearby (30-50 feet; 10-15 meters) then the Apple Watch will use Bluetooth with the iPhone to make the emergency services call.
If your Mother’s iPhone cellular plan allows for WiFi calling, AND you have enabled WiFi calling on the iPhone, AND you enable WiFi calling on the Apple Watch, then the Apple Watch can use WiFi calling.
NOTE: Setting up WiFi calling also involves specifying a 911 address during setup, as WiFi calling cannot use cell towers to provide location information to the 911 operators, and WiFi does not have a home address as a fixed landline would.
If out of Bluetooth range, but both the iPhone and Apple Watch can see each other via WiFi, then the Apple Watch can use the iPhone to call emergency services.