I'd much rather have the car sent to a wash bay that does underbody then have the wheels removed so they can clean the wheel wells. Give them a generous tip if you're picky on how they do it, so when you go back they will do a better job (hopefully)

Use a thick durable nylon brush. If it has plastic covers see if you can remove them, as sometimes the mud can accumulate inside the covers especially if you waded through flood.

Yep, it's very rewarding indeed.