First thing to do is open the drivers door and look for a yellow stick that states Passengers and Cargo not to exceed xxxx lbs". That is the max payload for your vehicle, but if you added anything after it was built you need to subtract that weight also. Subtract your family weight from the yeloow sticker payload amount, and that is what you have left for additional weight, including the tt tw (travel trailer tongue weight). Also figure roughly about 100lbs for a wd (weight distribution) hitch into the available payload.
How many bikes? If you have 5, I would believe if they alone are close to 100lbs. Firewood adds up quickly as well. We have 2 rubbermaid totes that are ~42"x 20"x20". Filled those weigh about 150lbs/each.
The main issue you will have with a growing family if the payload of your Armada, and the rear axle rating. On average, a tt needs about 12-15% tw of the total tt weight for a stable tow. Take the gvwr for the tt, multiply by .15 for the estimated tw. Is it lower than the amount you had left in your available payload? If not, choose a lighter trailer. This is a good starting point. The average person adds about 1000lbs to the "dry weight" of a trailer, which when it rolls off the assembly line usually weighs more than the "brochure dry weight". Our new Jayco we just got, brochure weight- 7600lbs, yellow sticker weight w/ propane and battery- just under 8000lbs (7937lbs or so), loaded, ready to travel (minus our twin 12yo boys stuff and no bikes, and all tanks, fresh and waste empty!) was 8860lbs, so after adding the boys stuff and the rear frame mounted cargo hitch w/ bike rack/bikes- about 9100lbs. At 8860lbs, we have a 1400lb tw (~15.8%).
I can not remember her name, but there was a member who started with an Armada ( I think it was!), and now has a hd truck. They upgraded to a hd, then upgraded again after wanting a bigger trailer!
If the 7800lb trailer you mentioned is "dry weight", there is no way you will be able to tow that safely with your Armada. At 7800lbs LOADED, your tw could be ~900lbs- 1170lbs or so.
I believe the Armada's wheelbase is a little shorter, correct? That is another challenge of a 32'-36' trailer. Large billboard for crosswinds with a short wheelbase tv (tow vehicle) is not a good combination.