If you do decide to make the move to a slightly larger tow vehicle, you might want to look into a hybrid trailer. Most start around 17', and the lightest weight. They are a real, hardside trailer that has bunkends that fold out of the front and back. We had a ROO 23SS, which had a box size of actually 20'+ and about 24' bumper to ball. One slide. Real bathroom....with a door! Kitchen, sofa, dinette. Obviously you won't get everything squeezed into a 17', but when you open up the bunkends you've just added about 7 - 8' of living space. Towing smaller and lighter, opened up much larger. You're still going to be dealing with the frontal limitations regardless of your choice, but it might be worth looking at some hybrids online and see if it's something that might work for your family. Definitely, the Patriot is not going to do it, but you might be able to go up a notch or two on the vehicle and allow for some wiggle room and be safe. Our 23SS, when fully loaded and ready to go weighed 5000# on the nose.
Have you given any thought to possibly finding a P/U crew cab that would do for the family? Might solve several issues if you could find a gently used one that would fit the budget and have factory tow and all you need to do this safely and without breaking the bank.