Answer: Dog poop is never a good idea in a veggie garden, from an aesthetic point of view. By removing the majority of it (along with some soil) I think you've done enough to keep your plants from being contaminated. Just to be on the safe side, I'd plant above-ground veggies in the garden and plant the carrots, potatoes, turnips, etc. in a different spot. The general recommendation is to keep feces from meat eating animals out of veggie gardens - this caution is normally for pigs, not cows, because we do recommend using aged cow manure as a soil amendment. If your dogs only eat dry dog food, table scraps and cooked meat, you have nothing to worry about. If they eat raw meat, there may be harmful bacteria in the soil.
Best wishes with your garden!
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