shimmying, shaking, and/or vibrating

I have a 2002 Ford explorer sport 2dr. 6.0L, with aprox. 69500k. I've recently installed 4 brand new tires. Two weeks after I took it on the highway and it was shaking and vibrating alot @ about 50-65mph. I just brought it back to have it rebalanced, took it on the highway again and is still shaking @ 50-65mph. I've also recently had my vehicle inspected and passed. All this within two weeks of each other. Just the other day the check engine light came on as well and remains on. Apon starting my vehicle it wants to stall out from time to time, only once or twice did it shut right off after starting.
Can you tell me what is causing the shaking,vibrating or shimmying? and why does my truck want to stall out and idle low?