Engine shut off when A/C turned on?

I am having the same exact problem in my 2001 Mercedes ML320 6cyl AWD. The car shuts off if Im sitting at a signal or if I park but leave the car idling and have the A/C going. But the engine ALWAYS turns right back on. But as soon as I come to a stop and am idling (with the air on) the car starts to stall out and turns off. It doesn't happen all the time. Actually, Ive noticed that it only seems to happen when I am low on gas too. Does that sound like the IAC?. At first I thought there was maybe an issue with the car overheating - I changed the thermostat, flushed and put in new coolant, checked for leaks in the hoses and made sure there were no vacuum issues or cooling issues. But the car isn't overheating. I changed the air filter. It didn't change anything though. The negative terminal strap clamp for my battery needs to be replaced, sometimes the terminal isnt solidly connecting with the negative/ground strap clamp, or isn't touching the battery terminal, and the car wont start until I pop the hood and readjust the negative connection on the terminal. I replaced the battery back when my car was randomly not starting. Figured out it wasn't the battery it was the terminal cover. But I was thinking that maybe something with power coming from the battery was causing my issue now. Thinking that the A/C was maybe too much since the battery isn't always getting the best connection (I'm currently waiting for the part to change the negative terminal). But its not an electrical issue. So it HAS to be something with fuel or air. Maybe fuel filter or the IAC right?. Or maybe spark plugs. Its been driving me absolutely INSANE trying to figure out what could POSSIBLY be causing this. And just when I'm about to take it to a shop, it stops happening.I usually do most of the maintenance myself on my vehicles. Ive been around and working on cars since I was a little girl helping my dad work on his dirtbikes/car/sandrail/etc. But I'm FAR FROM a professional.I don't even know if I would go as far as saying I'm at the intermediate level.I feel like there's still so much more to learn. Diagnosing is sometimes difficult but if I know what's wrong, I'll do a damn good job fixing the problem. If anyone could point me in the right direction or offer some suggestions, I would greatly appreciate it!
LJ