How can I send SMS messages from an iPad mini with cellular connection?

My mother has an iPad mini with a cellular connection.

We tried to send a SMS to her sister using iMessage but this does not appear to be working.

First I added her sister as a contact with the only contact info being her cellphone number.

However when I selected her sister as a recipient her name is shown in red and when I pressed send nothing happened.

Should this be possible?

I read that one can pair the iPad with an iPhone to get this working, but we do not have an iPhone.

I also contacted the mobile operator and the SIM card is ready for texting.

Is there some other app we can install on her iPad to get this working?
Or should we subscribe to a mail to SMS service?