Why does my car vibrate when its in drive and stopped?

Ok i really hope you guys can help me. I have a 2003 ford mustang base V6 it has dual exhaust from the headers to the tips, it also has a shift kit, cold air intake and its sct tuned. The car is fine when its moving but once i come into a full stop and im in drive or reverse it vibrates kinda unusuall. It does not vibrate in park because the rpms increase. I thought it was the bettery strugling to keep the engine on since the car has HIDs and i noticed when its raining and my wipers are on it vibrates harder. I really dont know whats wrong with it and i hope aomeone could help me.