I think you are confusing some people with the term wide angle. Your only 2 lenses are a 70-200 and 50mm right now, so wide angle to you is probably more like standard zoom to the rest of us. You probably want something like a 24/28mm - 70/80mm zoom. For $600 there are a few options.
If you have to stay Canon, you won't get a very fast lens for under $600. You can get the 24-85mm f3.5-4.5, the 28-105mm f2.5-4.5 or the 28-135mm f3.5-5.6 IS. All of those are reasonably sharp, have good build and USM for fast focusing. The ideal would be the 24-70 L, but you will be very lucky to find one under $1000.
If you want a faster f2.8 zoom in your budget, you will have to look at Tamron or Sigma. Sigma makes a good 24-70mm f2.8 Macro zoom and Tamron makes a great 28-75mm f2.8. Both rate pretty well.
And as to where wide angle starts, I would say about 30mm. ultra wide starts at about 24