Engine Shuts Off When Idle

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Hello, I have a Hyundai Accent 2003 automatic with a little over 170,000 miles. I have personally replaced all fuel injectors but I still have this intermittent problem of the engine shutting off. It occurs when my car is sitting in traffic or sitting for a long time at a drive-thru. I do not believe it's electrical because while the engine shuts off the radio continues to play. Typically when this happens, I shut off the car completely, then immediately restart it. Today is the first time that it did not immediately restart. I was sitting in a drive-thru listening to the engine and I could tell it was going to quit soon because, it sounded like it's "breaths" were drawn out, I don't know how else to describe it. The engine turned off, my radio was still on and I shut off the car completely and when I tried to turn it back on, I could hear the engine trying to turn on but it would not. I let my car sit for five minutes and I tried to turn it on and boy did it struggle to turn on! While it did turn on the car began to vibrate and it seemed it would shut off again so while I was paying for my order, I had the car in park and then gave it the gas. It seemed when I gave it gas it wouldn't vibrate as much. Anyhow, once I got out of the drive thru and on to open road where I can keep the gas going, the car leveled out. Now originally, I was going to just replace the crankshaft sensor because it's a cheap enough part but this is the first time it's vibrated during such an episode and I'm beginning to wonder if that means it's not the crankshaft and instead something more. Additional background information: I have an inkling that my fuel pump (?) needs to be replaced because when I was topping off my gas, my car would shake the same way it shook today. I have stopped topping off my gas and I didn't feel the shaking since, until today. My tank is currently half full so I do not believe it's the fuel pump that caused the shaking this time. Any help is greatly appreciated as I am on a very tight budget and intend to fix this myself. Thanks!