So hubby and I drove out to Colorado Springs, about an hour or so south of Denver this past August with his Ram 1500...we spent roughly $1,000 CDN in fuel (surprisingly cheap down there even with the exchange) and about $3,600 in hotels (we left August 1, got there on the 3, stayed until the 11th and were back home around midnight on the 12th)...we've been thinking of getting an RV for many years, however due to Covid, couldn't justify buying one...I'm a very picky person when it comes to hotels so we end up staying at the more expensive ones which is why it worked out to about $300/night after the exchange...with having summers off (and hubby's work allowing him to take up to five weeks off as well), we're thinking of getting one so we can just take off next summer (and subsequent summers as well).
The US is very different when it comes to travelling as someone has already said...there are a TON of places that you can "boondock" for free including national parks, rest areas, truck stops and even Walmarts...obviously you don't want to set up camp for a week in some of these places, however, if it's just for a night's rest while you're on your journey to a destination, then it's not an issue...there are also KOA Camps as well as other RV Parks all over the place that offer serviced/unserviced lots...not to mention the websites/apps that allow you to find a place while driving so you don't even have to preplan your entire route.
Storage is a big factor as someone else here mentioned...either you have space in your driveway (and good neighbours who won't mind) or you need a storage space (which can get expensive)...upkeep is another factor to keep in mind...and, as someone else mentioned, weight is a big one...for a family that size, you need a decent sized camper and although I'm not familiar with the tow limits of an Odyssey (although IIRC you said 3,500 lbs), you'll have a hard time finding something that lightweight that is going to offer you the space you want.
P.S...if anyone is selling or knows of a Grand Design Imagine XLS 22RBE for sale, let me know...