Hey Mark VA,
We can understand your concern over your mother with having a weak cellular signal, and are glad you though to ask Apple Support Communities about a possible solution. With weak cellular signals, if her carrier supports it, you can turn on Wi-Fi calling. This way, if the signal is too weak, it will use her Wi-Fi signal to complete her calls, or the call to emergency services if it's ever needed. Here's more information on Wi-Fi calling, and how to turn it on. Be sure to turn on "Allow Calls on Other Devices" so it's automatically enabled for her Apple Watch: Make a call with Wi-Fi Calling
This article Make calls using Wi-Fi on iPhone also explains: "In the event that cellular service isn’t available, and you have enabled Wi-Fi Calling, emergency calls may be made over Wi-Fi, and your device’s location information may be used for emergency calls to aid response efforts, regardless of whether you enable Location Services. Some carriers may use the address you registered with the carrier when signing up for Wi-Fi Calling as your location. When connected to Wi-Fi calling, your iPhone may not receive emergency alerts."
Fall detection is a wonderful feature, so let's be sure it's set up correctly by checking the steps and tips in the following resource. Note: If you turn off wrist detection, Apple Watch SE and Apple Watch Series 4 and later won’t automatically make an emergency call even after it has detected a hard impact fall.: Use fall detection with Apple Watch
Updates were also recently released for both the iPhone and Apple Watch. The current software version for the iPhone is 14.1, and for the Apple Watch it's 7.0.3. To see what's installed on her devices, tap Settings > General > About on both. If updates are needed, be sure to back up her iPhone first:
How to back up your iPhone, iPad, and iPod touch
Update your iPhone, iPad, or iPod touch
Update apps or use automatic downloads
Update your Apple Watch
Thanks again, and have a great day!