general problems of the 2016 Chevrolet 3500

I reported to my dealer charper Chevrolet Nov. 2018,I had roughly 23k miles,that my 2016 chevy 3500 had developed a wobble, shake whatever you could call it. They investigated and told me my tires possibly had broken belts the tires had plenty of tread left. I was told if I could deal with the shake till I get new tires so be it. I rode them till July 2019 got 6 new michelin 235/80/17 ltx a/t2 tire package. They rode ok still had a little shake to start then it got worse the more I drove. Let me say it never shook all the time it would come and go. Sometimes when I headed for work in the morning shake shake shake other times nothing. When going around bends shake shake then nothing. It is very annoying and needs attention. My dealer want to investigate more but I am being asked to fund the investigation. Where do I go from here? please advise me. Thanks fred w. Fallenstein.