Algae Pond Water

Algae ha taken over the fish pond. We have a sufficient pump and keep the filter cleaned almost daily. I've tried barely bales and they seemed to work earlier in the season, but once the weather got hot the algae got so thick it looked like pea soup. About three times a week, I remove as much as 30 gallons of green slimy water and refill with hose water. I pour the pond water around our flowers (but not our vegetables) to keep them alive. Nashville has not had sufficient rain in about a month and since the rain barrels are dry, I'm have to use the hose and city water (yuck) to keep the veggies growing.

Any suggestions on how to overcome this problem? I don't want to use chemicals to kill the algae because our dog sneaks a drink from the pond when my back is turned.