There is an obscure (to me before now) setting in what they call the "Custom Functions" that let's you force the camera to use 1/200th second http://www.ausphotography.net.au/for...ut-using-flash) where it would choose a very slow in low , causing blurred images due to movement.when in priority mode with flash. This totally solves the problem I had (see
From the 600D manual...
If you do not want a slow to be used, set [3: Flash sync.
speed in Av mode] to [1: 1/200-1/60 sec. auto] or [2: 1/200 sec.
(fixed)] in [7 Custom Functions (C.Fn)]