Making reservations for NPS or FS or State campgrounds does take some getting used to. You write "access" to parks, but I assume you mean getting a camp site. You didn't state your particular problem, but I'll take a stab. As a 2.5 year full-timer in the West, I will share that reservations in the Western parks are a MUST! Caveat = some campgrounds also keep first-come, first-serve sites for which you have to get in line VERY early (like 6 AM) and hope someone leaves. The feds use recreation.gov and states appear to use reservation.gov more often, many states have their own system. But they all work the same.
Get to the .gov page for your chosen CG. For NP, there will be a link under the camping info at the Park's website. Many parks have more than one CG. Enter your arrival and departure dates. Use the filter function to specify type of RV, length, what kind of hookups, etc. Then hit "search". Here's where you simply need practice of how to read the results. There is usually a "list" view and an "availability" view so choose which you want. I use the availability mostly because it shows me a 2 week calendar of what nights all the compatible sites are open. Sometimes 4 of the 5 nights I want are open for one site, another site will be open 3 of my 5, or any combination. Sometimes only FC FS are open. You just have to look at all the details.
There is also a map view so you can see where a site is in relation to roads, trails, bathhouses, water, etc. You have to read, read and read more. If a site is marked as available, click on the Detail view and read! Is it long enough, is it shaded or sloped, restrictions?
I have spent probably close to 100 hours using the online reservation sites, so I get the logic now. But I know what you mean about going around in circles. Use the back buttons on the SITE, not your browser back buttons. When all else fails, close the site and re-access, go back to the beginning - where you enter desired dates and then take the next steps. All you really need is practice, practice and patience till you get the hang of it. It can be frustrating till then.
Now the bummer news. At this point, getting NP reservations out West for this summer is a lost cause. FC FS may be a choice if you want to take a chance. In fact, NPS reserved sites usually fill up within a day or two of the 6 month advanced window. I notice now that SPs and private campgrounds are also filling sooner. I have had reservations for my travels up through Jan 15, 2022 since the end of April 2021. This includes NP, FS, COE, SPs and private CGs. And I had to put in a lot of effort to get all that together because of lack of availability at public CGs, full private parks, etc. Others may choose to travel differently, especially if they have smaller rigs.
Linda