Business & farm

Yes, you can claim those miles even if you have to go home during the day.  

Business Use of Vehicles

Also, your "home office" doesn't have to be a separate room.  It can be a designated space in your home that is set aside and separated exclusively for business use.  To take a deduction for your home office, you must regularly use "a portion of your home" exclusively for conducting business.  Also, it must be your principal place of business.  Which, in your case, it is.

This link may also be helpful Can I Take the Home Office Deduction? 

https://ttlc.intuit.com/replies/3302005