what I would probably do:
* I would show up with my family (if you can) and check all of us in (make sure that the luggage is checked in under your wife's (or kids) name, not yours
* I would afterwards cancel my flight/boarding pass (unfortunatley I had to change my plans - sorry, and naivly even ask, but not expect, any refunds). Don't be a no-show, be a canccelelling costumer
* I would not worry much about later charges to my credit card (you would anyway have 30 days to dispute such charges)