The key is to kill the queen. Put a couple of commercial bait stations which basically contain borax mixed with some corn syrup somewhere the dog won’t get at them but the ants will. Even if the dog did lick up a bit the amount of borax is too small to harm him. The borax disrupts the waxy coating of the ants which causes some of them to die of dehydration within the colony. Their bodies are canabalized and fed to the queen. She thus ingests the borax and desicates into oblivion herself which causes the collapse of the colony.
I’d be careful with the tumeric and cayenne since they could permanently stain surfaces.