That does sound strange. Two different systems with those messages, engine lights has to do with emissions and Stabilitrak is a separate system. Not sure if the same computer handles both, but sounds like the dealer needs to diagnose this one. There are many threads regarding the check engine, including some by me. I have had several components changed out and still no solution. It's in the dealership now, supposed getting a redesigned throttle body. Good luck. I love my car, but its a challenge at times, thankful for my warranty.