AC starts blowing hot air when I take a turn

Too difficult to determine in this forum. A local inspection by a shop near you would be my suggestion. Here are some ideas: https://repairpal.com/toyota-within-10-miles-of-richmond-virginia-23231

The wire is most likely loose or broken that connects to the heat control. Go to this site to find out how to fix it. I just fixed mine today. http://www.devalcourt.com/2010/03/fixing-2004-toyota-highlander-ac-and-heat-issue/