2007 Silverado Stabilitrak/traction control issue.

I have been trying to troubleshoot my Stabilitrak/Traction control system because of an issue that I have had for a few years now. I have replaced the front hubs and speed sensors and have also changed the read speed sensors. I have replaced the Throttle control sensor and when that did nothing, I changed the complete throttle body. The truck runs perfect other than the issue with the STK/ TCS light coming on. While accelerating, the truck is usually fine. When I brake or sometimes leave off the accelerator, the light comes on. I don’t lose any power and if I hit the gas and maintain motion, it will go off until I brake again. But if I stop or slow to a crawl, when I accelerate again I will move about 30 to 50 ft and there will be a huge jar which seems to come from the differential. the Jar is sometimes violent or sometimes its barely anything at all. but after the jarring… it continues perfectly without issue until I slow or brake again. while moving everything is fluid and smooth. shifting is perfect. No erratic RPM or power loss. I have replaced the sensors with negative reactions. does anyone have any help for me. anything will be helpful.