If you are an employee and you are asking about the tax year 2018 you are no longer able to deduct unreimbursed business expenses. Only independent contractors are able to deduct expenses under the new tax laws. Even in the past years you would have not been able to deduct commuting costs-just the miles driven while at work. In the past you could deduct miles driven between two jobs-now with one a W2 jog and one a 1099 job I am not certain.
If your second job is as an independent contractor then you would be able to deduct the use of your vehicle for that job. https://turbotax.intuit.com/tax-tips/self-employment-taxes/standard-mileage-vs-actual-expenses-getti...
