When shooting action, it's dangerous to use aperture priority. You focus on getting depth of field, and you typically forget about what the shutter speed is doing. If the lens aperture is too small and/or the light level is too low, the speed of the shutter slows down. This, in turn, translates into less-than-sharp pictures.
In a situation like the two puppies playing (the great Pyrennes is 10 months old and the cocker spaniel is 8 weeks), I opted for Program mode. This gave me the fastest shutter speed (minus 1/3 f/stop) given the lighting and the ISO. Because this was taken in shade, I used ISO 500. With Program mode, I got 1/640th of a second on the shutter which was perfect to freeze my playful dogs.
Teddy is the new addition to my family, and it's so adorable to watch him play with Princey who is about 50 times his size!