Thanks for the suggestions everyone. In broad strokes, here's the thinking to reply to a few comments at once:

1. We didn't want to use a phone-based solution because she doesn't always carry her phone in the middle of the night. This goes for carrying a button.

2. A LifeAlert system could work, but they usually involve buttons.

After talking about it, we realised that simply putting out a baby monitor or equivalent might be the most effective - she can shout at it and it will go direct. An alternative would be setting up a HA alert to broadcast based on a phrase (or a few). We'll weigh up the options but I'm leaning towards the former.

Thanks everyone! I appreciate the ideas - I think HA might not be the solution after all, but hopefully I can keep them from installing wiretaps Amazon Alexa in their house.