V.W.
Not having consulted an etiquette book on the matter, I would say that:
1) You do not need to send announcements to fellow graduating seniors. They are well aware of the event and fellow graduates. If they are at the same school.
2) Sending one per household is fine. Include Mr/Mrs and family.
3) It would be fine to send a single announcement to the "staff" at the dental office.
Relax mom. Even if it isn't done PERFECTLY (and who even knows what that is--someone always has a problem with something no matter what you do), it won't be the end of the world and you won't ruin your reputation or your daughter's.
Congratulations! Graduating senior with a job! WOO HOO! :)