Welcome to the forum! And thanks for asking about this! Its really important that you stay within ratings to have safe and happy camping experiences.
Here are the two "gotchas". MAX GROSS TRLR WT (LB) 9200, MAX TONGUE WT (LB) 920. The Jayco has a "dry" tongue weight of over 906. Loaded that will easily top 1200#, well over your 920# limit. Additionally its GVWR is 10,750 which far over your 9200# limit.
Never look at the dry weights of anything. They are fictional numbers when considering what the real weight weights will be when loaded. Those are the numbers you need to work with. And with 5 growing kids, your cargo is going to weigh a lot. You need to count their weight and the weight of all your stuff and subtract it from the towing capacity of the truck. Then pick our trailer based on that number. Realistically you looking at no more than a 7500# GVWR trailer (or probably a 6500 "dry weight" trailer). I'm not sure you're going to find a kitchen and a bunk house in that weight range.
All that said, I have knowingly towed close to my rated capacities so I speak from experience. Its doable under the right conditions, that is relatively flat terrain and short distance travel. But you can forget about mountains and anything long distance.
The ideal trailer doesn't exist. Every one has some compromises. I wish you the best!
