Do I need to claim a home office deduction in order to deduct business mileage?

My wife runs a cleaning business as a sole proprietor. In a typical day, she travels from our home to several clients' locations in our area and then back home again. There is no "home office" to speak of, other than our home being listed as the legal business address.

However, she doesn't qualify for a home office deduction at this time, as she occasionally uses our home computer or her smartphone for bookkeeping and does not store any inventory. Our home computer is used for both personal and business purposes (bookkeeping mostly).

My question is: Is she allowed to deduct business mileage for traveling from home to clients' locations and then back home again, even though she doesn't actually qualify for a home office deduction? Or would this be considered commuting miles (which are not deductible)?