I recently purchased a horse that overturns the 2nd barrel [even in competition runs].  What exercises, etc. can i do to help correct this?  TIA for any and all suggestions.

Squate drill may help but I would question what is happening on the approach, horses body position, your hands and body position. A drill can help but if there is an underlying issue that is not looked at, with speed the problem may return.

Happens super quick but your hand comes up on the exit pulling his face to the inside. Push that hand forward, hes working like a pro, trust that exit.

Go faster...