I will try to configure DND mode for her, but I'm not sure it will be enough, but it is worth a try.
The other problem about carrying it around is more difficult. She doesn't manage to carry her alarm around using a lanyard (it will be changed to a bracelet, this change is what triggered the idea to get her a wrist-phone too), so I can't imagine she will carry around her phone either. Maybe with a nice bag? Worth looking into.
Anyway, thanks for the DND suggestion, I will start with that.