Balance Billing for Invisalign Case?

Insurance companies have their own rules and change them all the time.  Any questions with those are up to them.  The fee to the dentist is what it is, regardless of insurance input, whether they pay or not.  You are fortunate to have insurance assistance at ALL for orthdontics.

Pre Authorization means that the insurance company authorized the payment for the treatment under the insurance coverage your father had at the time. The problem is sometimes insurance companies pay up front and others pay in increments.  Most of the time it is the latter. If there had not been a change of insurance plan, there would not be a problem. Unfortunately, in the end, the patient is responsible. The insurance is there to help you. People often look at dental insurance as full coverage which is not the case! Dental Insurance is not the same as Medical Insurance. It is just a benefit

Sorry to hear about your issues.  Unfortunately that can happen with patients who change insurance companies and ultimately the responsibility will fall on you to makeup the difference. A lot of time it depends on how the payments are sent by the insurance company.  Many times payments are made all at once which would have avoided the situation, quarterly or even monthly.  To make a long story short, you will be responsible for the charges.