How do you set up your TG-1?
Using the Super Sport selection seems to handle bright light and fast motion pretty well. I was trying to photograph some California vineyard roadside scenery from the car at freeway speeds (yes, I was the passenger!) and getting a lot of blur until I put the camera on Super Sport. I got a few bursts of extra photos I did not need, but it really helped with the motion blur problem.
Both my older Tough 6000 and E-PL1 do well with the canned Sport mode when I am trying to photograph my horses in motion.