Food you furnished to your household employee cannot be deducted (you are not a business, even though you have an employee). A better question would have been do you have to include the value of the food as income on her W-2? That answer is no too. Although fringe benefits are sometimes taxable, furnished meals fall under the convenience of the employer rule.
Regardless of whether the nanny chauffeur the kids in your car or hers, the travel is not deductible to you, even if you paid her extra (e.g. gas reimbursement). If she drove them in her car, she can deduct the mileage, subtracting any reimbursement you paid her.
