Work for company FT at home (remote) and drive 4-5 days per week to part time job in another state. Two different businesses. Can I deduct the roundtrip miles from FT to PT and back home?

yes; you , as an employee, may deduct work-related travel to a temporary place of employment as you require, other than your principal place of employment. Mileage between your principal place of employment and a secondary place of employment is also deductible.You may deduct reimbursed mileage if your ER include the reimbursement as part of your taxable wages on your W-2. You cannot claim a mileage deduction for travel for which your ER provide reimbursement not included in your wages.
The IRS establishes standard per-mileage rates which you may use to deduct eligible travel expenses to reduce your tax liabilities. This rate typically changes each calendar year. I gues $.55 for 2014.You may only deduct mileage if the total mileage deduction, when combined with other personal deductions, exceeds her standard personal tax deduction. The standard deduction is based on the number of dependents in your household. If you itemized deductions, including business mileage, do not exceed the standard personal deduction, youmust use the standard deduction. you can either deduct vehicle fuel and other vehicle expenses directly, or you can take auto-related deductions using a standard rate for each mile you drive for business purposes. You must choose the most cost-effective method to deduct vehicle expenses based on the number of miles you drive and the amount that operating your vehicle actually costs you.