If you are looking for state parks that aren't congested in CA that probably won't happen. If you boondock in the desert there are lots of very remote areas. Some depends on size of your RV. Easier to get smaller RVs into very remote areas.
Long Beach has a nice RV park. Golden Shores. Easy access to 710 then transition to century freeway for Marina Del Rey. It is a small but clean RV park. We lived in Torrance for 40 years. We stay there when we visit the area.
You probably won't see a snake but it doesn't cost that much to get him snake shots. Get shot and 2nd one few weeks later than once a year. Plus boarding during trip? Get a kennel cough shot. Many kennel require shot records before boarding.
I don't violate the law. Everything in my RV is legal. I'd invite the officer in an offer him a beer. JMHO they are looking for bad guys not fulltime RVers. As a retired LEO I never had time to hassle good people. Crooks kept me busy.
Everything I have purchased from CW in the last couple of years was returned because it was basically junk. I kind of wonder if they are buying assembly line rejects and pedaling it. I stopped buying anything from CW except basic mechanical items that you can visually see any defect. JMHO.
You can't get in until gates open usually sometime in May. May & early June are cool but you will see lots of wild life. More so than in the hot summer months. Roads ware pretty clear when they open the gates.
Don't blink or you will miss the whole town. They have a park on one end of town with a couple of buffalo. Probably the highlight would be the drive through the wind river canyon. Camping along the wind river for a day or two might be interesting. Not sure I would make it a high lighted trip from Wisconsin. We go through Thermop because it is the shortest gateway to I-80 from NW WY.