1999 Acura RL Running Hot

I started noticing last week that everytime I turned on my AC, the needle on my temperture gauge starts going towards the H and my car would run hot. I turn off the AC, but by then it's too late. I also noticed that my fans were not turning on when the car ran hot, so I was advised to change the sensor. When I had a "Mechanic" look at it, he stated that the sensor was not bad, yet I needed a new Radiator Cap. He also stated that when he checked the car, the fans came on. The cap was replaced and the car ran fine for 3 days. Yesterday, I had the AC on and it started doing the same thing. I turned it off and the needle on the gauge instantly dropped back down to a normal level, but soon shot back up and the car overheated really bad. Once I got home and lifted the hood, I seen the hose that runs from the Radiator to the Thermostat had a hole in it and Antifreeze was everywhere. So, I know I definitely have to replace the hose, but I am getting conflicting theories on what's causing the problem. I have been told to change the Thermostat and I have been told to get the sensor replaced. I don't know what to do, but I don't want to waste money replacing unnecessary things and/or damage my car in the process. Please Help!