The way I see it, you are mowing and running a business for $10/hr. What happens when you need a new mower or trimmer? Who is gonna pay for that truck that you want add on next year? As it is, the company is unable to sustain itself as you aren't making any profit at all and have no money for capital purchases, let alone expenses. You seem to have been concerned about paying yourself $10/hr instead of making a profit for the company. If you want to make $10/hr go to McDonald's. Also, just because you pay an employee $8.50/hr, doesn't mean you bill that. Employees are only there to make you money. If they don't make you money then you either have crappy employees or not enough work.
I am a solo part timer, If a yard takes me 45 minutes to cut, I charge $45. Its hard to hit that as you have to estimate how long it will take you to do it without doing it. That is one of those things that's comes with experience.
As for your current customer, I would cut them loose. Your loosing money everytime you cut it. Honestly, and I mean no harm by this, you should look into some business management book and/or classes. Anyone can mow a lawn, the hard part is running a business.