2004 VW GTI 1.8T slips gears when accelerating from a stopped position

I own a 2004 VW GTI 1.8 T, automatic, with 135,000 miles. Over the last few months this problem has progressively gotten worse. When I press the gas peddle to accelerate, it has trouble going into gear. Only happens with 2nd gear and only from a stopped position. The RPM’s rev but nothing happens as if I’m in neutral. I stop again and repress the gas peddle to drive and then it goes. Plus, sometimes as I am slowing down the engine will suddenly induce a major shift down with my rpm’s dropping to nothing and it feels like I get thrown forward a little as my car halts to 2 mph, i have to release the gas peddle and repress to stop it. Then tonight I noticed that when i turned off my air (heat) that was running, my engine suddenly worked fine. It was as if I never had the problem. I wasn’t sure if it was all due to the same problem, so I added it in as well. I am not at all “educated” when it comes to cars. I don’t believe my transmission is bad. I get mixed reviews saying either i need a new transmission, its a fuel sensor issue, or something else . It has been very difficult trusting a few shops around where I live so I wanted to put my issue out on some forums and see if anyone might have an idea of whats going on, especially since my research has turned up nothing. I check all fluid levels every week because of the high mileage and have all scheduled maintenance completed on a regular basis. The help is very appreciated, Thank you!