Mileage Deduction for a Private Tutor with Part Time Job as well

Here's the situation. I have a part time W2 job (no benefits included) for which I work about 19 hours a week. I also tutor privately at each client's house. 

 

During the week, I drive to the location of my part time W2 employment. After working there, I often travel direct to a client's house for private tutoring. Then from that client's house I either travel to an additional client or directly home. On weekends, I often travel direct from my house to client 1 and then usually on to a few more clients, before returning home.

 

My part-time W2 job and my private work are not related besides the fact that both involve tutoring. Can someone please explain if I am able to deduct any mileage from my private tutoring and if so what I would need to do. Also, if this involves claiming a home office exemption, would it make a difference if I am currently renting a room in a house? I do spend quite a bit of time at home, prepping for lessons.