Final Resolution Update:
AA accepted responsibility and confirmed that I was incorrectly denied boarding based on my itinerary and TWOV guidelines.
I will be refunded the fare difference plus all incidental expenses related to the change of itinerary as well as all MCE fees we paid for the trip.
Additionally, I was offered and accepted 400% of the one way fare for each member of my family. I was able to choose between a combination of vouchers and cash with vouchers being a higher value.
I am thankful and relieved that AA made it right in the end. I will say that it took a plea to the Social Media department (specifically twitter) to get someone to respond to my complaint. All responses I received from the online submission form were completely boiler plate sorry you had a problem. It wasn't until the twitter team read my complaint and forwarded it to a specialty department that my complaint got to the right person.
I appreciate the support from most of you and particularly to those who reached out privately.
Jason