Car has season problems. Warmer weather, the car doesn't "turn over" and stutters. Colder weather, some type of toxic smell coming from the heater. Going in reverse makes the car shake. All these problems are intermittent! Never happens at the dealer!HELP

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I've been dealing with Chrysler headquarters and not getting the help. 2 dealerships claim there's nothing wrong with the car. I've had problems with the started and now I think the transmission will go. A 2013 shouldn't have these problems! I have 2 babies. I have to turn the heat off and freeze because I don't want them to breath that toxic smell. It's almost a burning plastic type of smell. The battery is always dying. I would love to sell this car privately but I would feel horrible to sell it with all these extreme issues. Is there a class action lawsuit?? I want them to buy this car back from me. I spent way to much for a crappy car! Anyone else have that heater smell? Or does your car have a "hard start?" What could it be? Only 25,438 miles.