Your every other night plan will not work very well, especially when you're going to be in a pickup camper. As others have mentioned, there are limited places where you can legally park overnight, especially when you're in a National Park setting. Perhaps more importantly, when you're boondocking, you really can't appear to be camping - as in you can't have chairs out or anything like that. The amount of space you'll have inside a truck camper is really quite small, with almost no room for 2 people to move around. If you're not in a campground and are confined to that small space, I'd expect a lot of "friction."
I would also warn that a truck camper will itself be a challenge considering the time of year you'll be camping. You're going to be still seeing very cold temperatures, and even into May and June, it could easily below freezing overnight in mountain areas like Yosemite, Yellowstone, and Banff. I don't know what kind of heating system you'll have, and RVs typically aren't very well insulated anyway, so that will be another issue to keep in mind.