“I do know that my car when stuck in very little mud will basically shut down”
That sounds like automatic traction control taking over on you.
I ran into that one icy night trying to spin a fire engine around on an icy road to prevent sliding down a hill. I finally got it done.
When you are in that situation, you are supposed to turn off automatic traction control.
Yes, it’s very frustrating! I had to call a wrecker to tow me ten feet out of very little mud on an interstate service road in pouring down rain.
Not too many years ago I could have easily gotten out without the wrecker!