You’ll need to spray the area with clover with Bonide Chickweed and Clover Killer. You’ll need to spray where rain isn’t predicted for a couple of days. The killer needs to sit on the leave of the clover and other weeds for at least 24 hours to work. It kills the roots but is absorbed through the leaves. After the two days, you can water the area heavily which will wash the herbicide into the soil. Since your dogs eat the clover, I’d keep them off the lawn for the week and a half or so that it will take the herbicide to kill the clover.