I use my 450d with a Canon 50mm f/1.4 for photographing my 4 year old. The lower the f-number, the wider the aperture, the harder it is to nail the focus (I've got hundreds of blurred shots from trying to shoot at f1.4)
There are a number of things that have helped me get better pics of my son. The best thing I did was to buy a 430EX ii flash. The camera focuses much faster in low light with the flash and being able to bounce the flash off the walls produces a much more natural image. The other thing was to just use the centre focus point in 'one shot' mode.
As regards to dressage, good glass that works well in low light costs. You could try a 50mm f1.4. Set the aperture nice and wide say around f2 and the the ISO high enough so that you can get a fast enough shutter speed (i'd take grain over blur any day of the week). I've taken shots at ISO 1600 with my 450d and they looked quite grainy but I managed to remove the grain with software (NeatImage). You want a shutter speed of around 1/100 or faster i'd say (with a 50mm lens on a cropped body).
When the kid or kids are in bed, get the camera out and experiment.