I am not sure if you mean you are having trouble finding available pitches [not already booked up] or campgrounds themselves.Quote:
Finding camping spots in the parks or at least near enough to feel like you are there that has a shower and bathrooms seems very difficult
You can use the National parks booking site at recreation.gov and the established sites have toilet and shower blocks.
These are as follows, Yosemite> lower,middle or upper pines campgrounds, Zion> Watchman campground and Grand canyon> Mather campground. All in great locations within the parks and easy access to the free shuttle bus and amenities.
If you know your dates and can find an available pitch book it as soon as you can. If you have no luck within the parks you should find something close by using the search engine but I recommend staying within if poss.