Car hesitates and feels like it wants to due when turning steering wheel. Any thoughts?

I will try to be as clear as I can, thank you in advance for the answers.

So when I turn my car on in the morning and night (mostly when it's cold out) the engine dies right after I put it in gear (not reverse) I can go in reverse just fine but as soon as I put it in Drive it dies, I can start it right back up again and it drives fine after that.
Also, when I turn on the car in the morning or at night (with just the radio on) if I turn the steering wheel in any direction the engine looses power and the battery light turns on and off as the engine tries to rev back up to normal, it kind of feels as if I was accelerating every other second but with very low power.
About the car turning off, my mechanic told me it could be the idle air control valve but I replaced it and it still does the same (although I should mention I replaced it with one not made specifically for my car)
I have thought of the alternator but I'm not sure if it can be that or any other component.
Thank you for your answers and time.
My car is a 2004 Ford Crown Victoria Police Interceptor I replaced the idle air control valve with one made for a 2010 Mercury Grand Marquis.

Install the correct IACV. Get the MAF sensor cleaned or replaced. Clean the intake. Check for vacuum leaks. Check if the alternator is charging. Check fuel pressure. But before you do anything of the above, get a tune up.

Ford IAC valves are pretty interchangeable. But not all of them are. If it was for the same engine family it should be alright. I used a Mustang V8 IAC on a 89 SHO (3.0). The interchange books said they were the same.
There's a pressure switch on the power steering pump. The purpose of that switch is to increase idle speed when the steering wheel is turned if the engine is at or near idle. This switch might be disconnected or bad.

This problem is usually due to the IAC valve that you replaced. The one you got should be OK but you should double check with another auto parts store that it's the correct part. If that's not it, clean the MAF sensor and make sure you've got a reasonably clean air filter and no leaks in the intake system downstream of the filter. And lof course, make sure a basic tune-up has been done before chasing other possibilities. One problem might be a weak ignition coil. I believe the Interceptor has two of them. If one is going bad it can lose its idle charge and that can cause a weak spark, causing the engine to falter or stall at idle when any type of load is put on it Even the power steering pump is enough of a load when turning the steering wheel. At about 40.00 apiece you might try replacing one first and then switching positions with the other to see if it makes a difference. If you get new coils, be sure to also replace the small capacitors attached to them.

HI age has taken it's toll on this old car. That and mileage over 150 k miles would be mu guess. Mister ford designed his cars to last 8 years or 100k miles which ever comes first.

Have the codes scanned, even if the light is not on there could be codes stored. Sounds like a vacuum leak or something called a "power steering pressure switch". It sends a signal to the PCM when the power steering pump is loading the engine so that it can bump up the idle and prevent stalling. It's usually mounted on the high side hose of the power steering pump.