You don't necessarily need to have to pay for cell service or a sim card. Any recent model smartphone with WiFi (i.e. any cheap Android phone) can be used to set up a new Echo device. Some tablets will work too, although I've seen certain features are not available in the tablet version of the Alexa app.
The important thing is the Echo device should be set up using your mum's own Amazon account. That way, anyone who wants to contact her via drop-in will be connect to her and not you.