Sending a text to another Mac user is not working with just their email address.

My mother is 80. She is not keen to have an iPhone. She has a flip phone instead. However, she does have a Macbook Air and uses messages to contact me to my own Mac or my iPhone. Lately, however, communication in this manner has been a miserable experience. Messages always default to her phone number, which obviously isn't on macOS or iOS, so I'm constantly having to reselect her email for the bubble to be blue. To solve that problem, I have deleted her home and cell numbers. Now, the system is forced to her email address. Yet, that isn't solving the issue as I thought. I'm still getting messages that are "undeliverable". What on Earth is causing this?