Hi
Only you can work out how much you will have along. We don't really know much about your situation. We are only guessing about a lot of things.
Are there two of you or eight of you? If it's eight, are four of those dogs? If so how big? How many bikes will you bring along and what type? Do you fish and need a boat? Do you cook out a lot and need to bring the smoker? ..... lots of very specific details that might apply to me but not to you.
If "living in it in the summer months" means taking off June 1st and returning home September 1st that's a bit over 12 weeks on the road. Will you be urban camping ( and eating in restaurants / grocery shopping multiple times a week) or will you be boon docking in the middle of nowhere? ( and hauling a couple weeks food / water /clothing along). You can fill a lot of space with a couple weeks supplies.
If you will be camping off grid, where will that be? The Gulf Coast in July will be a bit crazy without A/C. To do that off grid you will need a pretty big generator (maybe 100 pounds worth), fuel, and other bits and pieces.
How cozy do you like to be? A 22' is not all that large. Spending time outdoors is a fine way to deal with this. If there's a lot of sun or rain or bugs, some sort of tent like structure is probably a really good idea. If you have a bunch of outdoor gear (bikes ....), a second tent-ish thing might also be a good idea for storing that stuff. Those tents need to ride somewhere. If they are wet when its time to go, they still need to ride somewhere
( I have a *lot* of experience with that part).
The weight of all this matters as much as the volume. There are an unfortunately large number of SUV's out there (and indeed some trucks) that just about max out on weight when you put a full set of passengers in them. They put stickers on the door post these days telling you what the real capacity of *that* vehicle is. Trust only that sticker. The Internet will not help you here ( = the Internet numbers never include all the details and will be higher than the real ones).
Regardless of SUV vs truck, you want it set up for towing. That includes mirrors, brake controller, hitch, and suspension upgrades. Getting all that on a truck is pretty easy. With some SUV's the only way to get the full set is to do some customization. There's nothing wrong with that, it just means a bit more work.
If you are out and about for the day and it's a rainy day (stuff happens), you will come back with a bunch of wet clothing. That needs to hang someplace to dry. Same with muddy boots. However you set things up, you need to allow for this to happen and *still* be able to survive in the trailer.
Depending on region, you will need a range of clothing. There are parts of the country where a parka is not a crazy thing to have along in July. Hiking boots make a *lot* of sense in some areas and no sense at all at the beach. We travel with one set of "fancy cloths" ( = coat and tie / dress). An unexpected family event while out traveling showed us the need to do so.
If you are away from home base (or out a lot), stuff breaks. That means spare parts and tools. At the very least you need to have a torque wrench for the lug nuts on the wheels *and* an extension *and* a racket handle for the same nuts. Do you need a torque wrench that will handle the bolts on your hitch? How about a rivet gun and rivets? Towing straps? Multimeter? Tire pressure gauge? Spare batteries? Study up on each and decide.
You will need some way to chock the trailer when it's parked. You may use multiple methods. (We use X-Chocks and wedges). It is a good bet that leveling blocks will come in handy (possibly several sets).
Water hookup / sewer hookup / electrical hookup can range from "easy" to "who designed this place?????". We carry multiple sewer hoses, a couple hundred feet of water hose, and almost a hundred feet of power cable. All have been used at multiple campgrounds over the last couple years.
So lots of twists and turns. Even if you had a fleet of trucks, you can't carry *everything* with you. You will pack what you think you need. When you get back the question of "why in the world did I bring this?" will pop up. After a few trips things will begin to settle down.
Bob