Sometimes when I start my car the engine light goes on then I see Trac off and the little engine light on the far right goes on, which means when I start accelerating the car hesitates a couple of times before it lets me go slowly. It does not always happen but its been happening more lately. My mechanic says it could be the acceleration pedal. Its driving me nuts!!!

 

Time for a new mechanic. He should hook a code reader to it and tell you what the actual problem is.
From what you described the car is going into "limp mode" or "reduced power mode"
gas pedal, throttle body, plugs, coils, all cause that. Oh and faulty wiring.

 

Get the battery load tested while you're at the auto parts store.

 

Indeed, get the codes, pxxxx. Not the text description of the codes. The actual codes. Post them here and we will try to diagnose. My scientific wild-*** guess is one of the throttle position sensors is reading improperly. There are dedicated codes that will indicate that if it is the problem