mmyk72

the bathroom issue is always the 1 thing that stresses me out when visiting China. The major attractions in Beijing actually have relatively clean facilities. The lesser known sites will be 50/50: either the WC is clean due to not many people using it, or it stinks due to no one cleaning it. Once you go away from Beijing, finding a clean WC becomes more challenging. I've come across many that stinks so bad I can't even go near the door. I've used some that have no door for individual stalls but the men/women sections are separate.

Tips that I find helpful:
Wear 'real' shoes, not flimsy flip flops. When you have to walk in those wet and filthy WC, you will feel better if there is a real separation between you foot and the floor. I prefer sneakers.
If you wear pants, imagine having to squat with them and make sure they let you do that easily and not drape all over the floor while you are down there doing your business. I have worn athletic pants with the elastic around the ankles. For regular pants or jeans, I'd roll up the legs just to be safe. Afterall, you don't get to do laundry as often when traveling.
Sometimes you can't avoid the real stinky WCs. It helps visiting in the winter so I'd pull a scarf or my turtleneck over my nose.
Go use the WC as soon as you find a clean one. You never know if you'll get lucky again.

evecolorado

Foggydoggy, we travelled the same route you will, and didn't find any toilets we had to walk away from (like I had to do at a truck stop in the desert in Egypt), though some were stinky with wet floors. Like Leanna says, "Quite often there was a line of stand up toilets and then at the end a sit down one for the handicapped", so if you want to sit, make sure you look for the handicapped one. And like others have said, keep TP in your pockets, as well as wetwipes, and double check before you leave the hotel in the morning that your daughters have done the same. mmyk72 gives great advice in the "Tips I find helpful".