The August Smart Lock is one of the best connected locks on the market right now. The lock itself is Bluetooth only, so Mom can only control it locally out of the box. Throw in the $50 August Connect accessory to bridge it to WiFi and Mom can control front door access and keep tabs on who's coming and going from anywhere.
Cree's Connected LED is another Editor's Choice winning product. We like it for the quality of its light output, its programmability, and its low price. If your Mom is into the idea of a smart home, this is the first recommendation we'd make for smart lighting.
Icontrol's Piper NV is an all-in-one security device that doubles as a smart home hub. It houses a night vision-capable security camera, a host of sensors (temperature, noise, humidity, light...), a speaker, a microphone, and a siren. It will also let her store saved video clips in the cloud for free.