Which SUV is limited to 3500 that you're looking at? One of the lowest tow ratings for mid-size 4WD's is the Honda Pilot at 4500lbs, which is what I have. 3500 either has you in 2wd options or compact SUV's. Compacts are no good for towing high wall campers. Pop ups, just ok.
It also sounds like you will be traveling long distance a couple times every year. That means you should have more tow rating "cushion" if you will. You wont want to tow near max as I do for common long travel. Some use the 80% rule in cases like this. But I stress NOT to use GVWR to shop for the trailer. The GVWR is the MAX the trailer can handle, not the weight you will ever load it to. Shop by "shipped" weight when possible, and over estimate the weights of things you will load up the trailer with. That's will be the weight to be slightly over when shopping for the TV.
For campers, I bought a Gulfstream Visa. Their 19 foot options are what you are looking for. They had some under rated axle issues, which has since been corrected with high capacity axles. I almost bought a 19' to tow with a Honda Ody, which again would have put us right under the max of 3500lbs, but my wife felt it was too small for 2 adults and 2 kids. She was right. We could not deal with anything smaller than our 23 foot. You're lucky it just you and the wife!