Bottom line is that this is not an IDB and therefore there is no IDB compensation, e.g. 400% of the fare paid for that CLT-LHR segment, capped at $1,350 and paid in cash.
A complaint to DOT will not result in individual action against AA and, even if DOT were to fine AA (which it rarely does for one off's) none of that goes to OP or his family.
OP's wife should send a polite, but firm note, focusing on the fact that she agreed to the VDB conditioned on a specific routing and even then a backup specific routing, neither of which AA was able to fulfill. AA will likely issue further vouchers in addition to the $550 likely issued already.
For the benefit of others:
1. Don't accept VDB without a confirmed seat on the reroute. Entirely possible that there was a seat when offered but somebody else changed, SDC'd or purchased it while the original flight was being processed. At a minimum, have the GA confirm that he has held the positive space (which he can do).
2. Ask for a supervisor. In this situation, a supervisor could have sorted this even if it meant additional compensation to others to make space for the family.