I think you will find shipping clothes home will end up costing more than doing laundry. I generally hit the laundromat every 10 - 14 days, using a campground one if it is available, but more often a real one in the nearest town that has larger machines. I do have the advantage that my trailer is small enough that if I stop before hitting a campsite, I can usually park it in the laundromat parking lot so I can hang out in the trailer in far more comfort than the typical laundromat.
If I am not towing, I bring my iPad & a good book & the time flies...