Firstly, even though you paid her less than $600 as a subcontractor, she is still required by law to report that as self-employment income and pay taxes. You may get away with not reporting it but that doesn't make it right.
As to the use of a personal vehicle partly for work, it depends on if you are preparing a business return (1065 or 1120) or if you are preparing a persona return with a schedule C. If you are preparing a schedule C and if you use "your" personal vehicle partly for work, you can deduct your work expenses using either the standard mileage rate method or the actual expense method, presuming you have the necessary records and logs.
For income tax purposes, if you are married filing a joint return, then you are treated (for tax purposes) as joint owners of all your personal and real property, even if the title is in only one person's name. If you drive your wife's car as part of your work, you can include your wife's car as a second vehicle on your schedule C and deduct the expenses by the usual methods, assuming you have the necessary documentation.
But if she drove the car for work against her $500 of income while you drove a different car for work against your income, then she would have to deduct the expense on her own schedule C.
However, if you are preparing a business return, you can't directly deduct expenses for any personal vehicle, but you can reimburse yourself for the business use of your vehicle and the reimbursement is a business expense. Then the reimbursement is either taxable or non-taxable to you personally depending on which set of reimbursement rules you followed.
