Please provide more details on you Suburban. I believe that we are all trying to help you. It is likely that with the three of you in Burb and trailer that you will be over your payload and combined gross vehicle rating.
Now, I did pull my trailer with the 3/4 ton (2500) version of the Suburban. It did fine, but had the payload and power. I have towed mine with a 1500 vehicle a couple of times, less than 50 miles. It is capable. I even made it up a hill. It was only me in the half-ton. I would not go further or take the family in a half-ton.
If there is no way to undo the trailer purchase, you may need to look for a different tow vehicle. Prices and conditions vary for tow vehicles, and what you are willing to use to travel. A Express 3500 can be had for a decent price, has roof rail airbags for rear passengers, has over 3000 lbs payload, and could tow the trailer. I purchased a 2014 last year with 2 years warranty and maintenance for under $25k. It had under 30k miles. It may not be the most exciting vehicle, but it serves a great purpose and has room and seating capacity. My 15 year old is getting very good at driving it, and will probably be the vehicle she drives.