Sorry to hear about your mother.
As someone who requires this kind of device myself, I’m happy to report that the market has really improved in the last 10 years, and there are now a number of devices of this type, quite inexpensive, that work very well.
This was recently discussed in the following topic. Make sure you follow the links there, including to the consumer reports discussion. Those are all lanyard devices.
Although The use case that initiated that topic is about someone who fell and blacked out, all of the commercial solutions for that problem also have a manual button that can be pressed to initiate the alert on demand, so they also solve your problem. 