EDIT: To anyone that finds this via search, the last link Jon provided (https://stackoverflow.com/questions/36437055/qsqlrelationaltablemodel-additional-related-columns/69987711#69987711) seems like the best approach

EDIT2: Unfortunately, although though the link above provides a great way to view data, there is no easy way to edit (or insert into model). Recommend going with a one-to-one relation.

Looking through the documentation I see I can set a relation to a field, but will a change to the patient_profile table in the database trigger the appointment tablemodel to update?

Absolutely not! Neither in Qt models nor in the SQL database.

What you are supposed to do with a foreign key is not store further information from foreign table columns also back in the referencing appointments table. This is one of the "fundamentals" and relational databases.

An appointment does not have a first or last name. Only a patient has those. If looking at an appointment and you want patient information you are supposed to use the foreign key to go get that.
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For your second question, Google for qsqlrelationaltablemodel multiple columns, that is what you are trying to do here. I don't think Qt/QSqlRelation handles this for you. Have a look through the suggestions at e.g. https://stackoverflow.com/questions/36437055/qsqlrelationaltablemodel-additional-related-columns. There are others (e.g. https://stackoverflow.com/questions/35536730/qsqlrelationaltablemodel-two-references-to-the-same-table-same-foreign-keys), so far as I can see all in a similar vein. Note that with these solutions you end up with your appointments table being not editable. Or perhaps, per the approach in https://stackoverflow.com/a/69987711/489865

There is only one problem if you want to edit values through a QTableView: You can edit other columns, but if you try to edit the related column, the model does not know what to do.

A follow-up question, since I want first_name and last_name to be mapped as well as patient_id, but only patient_id is guaranteed to be unique...how would I set that up?

appt_model.setRelation(1, QSqlRelation("patient_profile", "patient_id", "patient_id"))

That would map patient_id from appointments to patient_profile, but how would I set up the first_name and last_name...would I need to restructure my appointment table to something like this?
appointments

• appt_id
• patient_id
• patient_id_first_name (value is the same as patient_id)
• patient_id_last_name (value is the same as patient_id)

appt_model.setRelation(2, QSqlRelation("patient_profile", "patient_id", "first_name"))

I'm a bit hazy on this subject so any advice would be appreciated.