Does her psychiatrist do therapy with your wife? or just manage medications? Most psychiatrists I have seen just manage medications and charge for any out of session contact. Phone/email/text, anything.
My therapist and I text. Nether of us like email, because it's not secure. Text tends to also be more brief than email. We text 1-2 times a week for matters other than scheduling. It's brief, but helpful. It's like a check in.
If they are communicating outside of sessions every day all day, then that would make me think maybe something is off. My first concern would to think that she isn't getting enough support in session and needs more sessions.