One of the biggest challenges when you're camping is getting everybody off to the shower with everything they need and having them return with it.
Putting together a basic shower kit is easy. Start with a Silverware Tote/caddy or other waterproof type carrier. The plastic baskets that are sold for carrying around cleaning products work well if you can find a small one. It's best if it has a handle on it. Look for one that has holes already in the bottom of it and some type of feet. If you can't find one with holes in it, get some handy person in your life to drill some small holes through the bottom of each section of the carrier.
Fill each compartment with the things you need in the shower/bathroom. Be sure all of the items you've chosen are waterproof.
Liquid Shower Gel
Toothpaste / Toothbrush
Add a couple of Jumbo sized binder clips so you can easily clip a scrubby(ies) to the tote.If you find a tote that's large enough you can even carry a pair of cheap shower shoes for each member of your family right in the tote. They can wear their regular shoes to the shower, but use the shower shoes while they are actually in the shower. This will help to protect against foot fungus in a shared shower.
One other thing that is great to have are a couple of small "over the door" hooks. These will allow you to put them over the stall door so you can easily hang clean clothes, towels, etc. in the stall with you. Some facilities already have hooks in the stalls and some don't (or they don't have enough.)
When you return back to your campsite, put the tote on an uneven surface so any water that was trapped in the tote can easily drain out through the holes in the bottom.
This whole system works best if you always keep it loaded and packed with your camping supplies. When you get home from a camping trip, check the contents and reload or refill whatever you are low on. Then pack the tote with the rest of your gear. It will be one thing you won't have to worry about next time you pack up.