Towing with P235/75/15

[79blazer]

I have Mohave tires on the front and Michelin LTX M/S 235/75 SR15 105S SL on the back. They are rated about 2000 pounds at 35 PSI. Driving empty it is challenging to drive straight. It tugs randomly right or left. I Towed a 2800 pond car on a Uhaul trailer and "leaving something to be desired" is putting it mildly. It is okay at 40 MPH but it fishtails going straight with no wind at 60 mph. The back end handles so bad under load they feel like they are flat. With actual truck tires does that help much? I have a short wheel base. Well though the answer seems ovious, Better tires like Pirelli's Scorpion ATR is 2337 lbs. at 65 psi Is only 300 pounds better weight capacity than what I have now. Also gas milage is a priority. I don't drive agressivly so I don't need wide tires. I am just looking for some advice, before I spend hundreds of dollars on new tires! Would a differnt tire size help handling when towing? I don't want to have to buy new 16 inch rims if I don't have to. thanks