Shift 2nd gear when the gas pedal is pressed

From a stopped position, what would cause the engine not to shift into 2nd gear when I press the gas peddle to accelerate, only when stopped? 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 lately trusting a few shops around where I live and money has been extremely tight lately. I was laid off from my job a year ago so I can’t afford to pay for 50 diagnostic tests to fix everything that has nothing to do with the main issue! A year ago, all the testing wouldn’t have been a worry.

I wanted to put my issue out there and see if anyone might know what’s going on so I can have an idea of what needs to be checked out or done. 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!