Troy,
Your diagram seems to match your explanation of the relationships.
Quick Base can handle way more complexity that your diagram so no problem there. Many join tables are OK.
You can choose to make a relationship where 1 Clinic has Many Nurses. That will help because when you go to make a Home Visit, you will be able to use a Conditional drop down to choose the nurse as it can be filtered down to only showing the nurses associated with that Clinic.
As for what a summary field is in this scenario, it is still still a summary like a total or count of records below it, but it cannot easily summarize up any text fields like nurse's names. But that can be done with reverse relationships if the expected number of records to be "summarized" is reasonably small, like say 6 child records.
