Answer:
Commuting refers to travelling from your home to your workplace. It generally refers to the distance that people generally travel to get to their office or any type of workplace.
While business travel refers to not only leaving your house to go to work, but actually going somewhere else to perform your regular business activities, e.g. going form one state to another to close a sale. In order for business travel to be effectively recognized as such, it must be necessary for your business activity and it should last more than one ordinary workday.
In this case, your client continuously leaves his house and goes form one state to another performing his normal business activities. This perfectly fits the IRS's definition of business travel.
Initially, you can try to solve this issue with IRS Office of Appeals (since you are right), but if that doesn't work, then you can go to Tax Court.