I use a cheap-o brush from any house cleaning aisle at Target or WalMart to scrub the tires. The wash mit only gets used on the actual wheel and I just rinse the mitt and let it air dry.
I wash my "messy" job towels separate from my body towels.
Not exactly tar remover but I've found Meguiar's APC, Super Degreaser and sometimes even Wheel Brightener to work. It can take a few tries and good agitating to get it off but I've found them to work really well. I also carry Stoners Tar Remover and works well on most cases.
I'm pretty good about cleaning my wheels on a weekly basis and even waxing them so cleaning them is a breeze. Even with my aggressive brake pads I'm able to get them really clean. After I'm done blowing them I do go over it with a black microfiber towel and detail spray and touch up anything I...
Try using a second bucket for your wheels and rinse off with your spray water bottle. At least that's what I do in my garage at my apartment complex and it works really well. I use Megs Non-Acid Wheel Cleaner, barrel ez detail brush and regular lug nut detail brush. I also blow the wheels off...