This response is provided based on the information you shared and should not be used as the sole source for making a decision. You should seek guidance from the chain of command, IG, JAG or other certified agencies before making any decisions. How you chose to use this information is totally up to you and is your sole responsibility.
Great Question! Bottom-line upfront according to finance and travel regulations (I don’t know the specific regulation; you can check with the IG. It may be called the JTR…Joint Travel Regulation), the government is required to compensate you or provide a vehicle for the commute.
If you are normally expected to report for duty at one location and then you are placed on temporary duty at another location the government must provide you a vehicle or method of transportation and/or reimburse you for the travel with in and around mileage or another method of compensation like train tickets if you can commute by train.
If you are having an issue you might want to consider speaking with the IG and/or JAG to facilitate a solution.Hope this helps to some degree.