It sounds like you need to negotiate at the very least for the manager to offset your road expenses, and give a premium for the extra windshield time. Is this way out of the norm for a typical daily routing? Is it a fluke route? If this happens all the time, I sure hope that you are making enough good money most of the time to let this one wash through the cracks as a "favor". It all boils down to the root decision of "what else could I do to support my family?"
If its an issue of just being aggravated over the ultimatum, then do it, and be done with it. If its just constantly "taking one for the team", but coming out of your wallet, you will have to count the costs, and see if it is negatively impacting your family's financial situation. It still comes down to whether or not you can find a job that matches the take home pay or not.
You know your situation better than anyone else. Take some time and think it through.
Hope the best for you,
Jeff