I'd venture a guess that you'll gain little, and be on the edge of safe operation. Even a small Hi-Lo (like a 15') from the early 1970's weighs over 2100 lbs. You'd need to get rid of 30% of the weight, and that doesn't account for adding a small bathroom. Much of the weight is in things that can't be removed....frame, axle, wheels/tires, hitch, floor, walls, roof, windows, plumbing, wiring, refrigerator, air conditioner, lift mechanism, etc. You can only remove so much!
Then, you start adding stuff. Water? The small bathroom? Then you need gray/black water storage. Pots, pans, plates, kitchen utensils, dish detergent, windex, kids toys? For sure you'll need food and clothes and even if those are in the car, they start adding up to the car's overall capacity for towing......and more importantly, stopping.
I think it's a stretch......but others may have a better idea for you.