In the US weather information is broadcast 24x7 on 7 different frequencies around 162 MHz, if there is a severe weather warning or other emergency then the normal weather information is interrupted and two different alert signals are sent. One alert signal is a newer digital/analog packet and the other an older 10 second 1050 Hz tone. How the weather alert radios (receivers) with alert capability respond varies depending on the receiver and how it's configured, but typically the receiver is left on but the audio is muted (squelch closed), when the alert signal is received the audio is unmuted (squelch opened) so the message can be heard. This is basically the same as setting a digital or tone coded receive squelch on a ham radio, unless the sender transmits that tone it won't open the squelch of the receiving radio. Some GMRS/ham radios with weather alert capability will switch to the weather frequency if it was tuned to a different channel when an alert is received, which is basically the same as the 'dual watch' capability of many GMRS/ham radios - monitoring two different frequencies and it switches to the one with activity, or to the one set as the 'primary' channel if both have activity.
So guess I'm wondering why you wouldn't just use a cheap Chinese ham radio as the alert receiver? Seems to me just about any ham radio has all the functions you're looking for. If there's a concern the user might inadvertently change the settings, then a part 90 radio that you can program to a single frequency and squelch settings, and disable the transmit and front panel programming so they can't transmit or change anything. I think the $30 Baofeng UV-82C allows that, or if not then I know the $70 Puxing UV9R/973 does.