What can I use on Creeping Charlie in our yard that will not harm our dogs?
If you don't have too much of this weed in your lawn you could try removing it by hand. It is shallowly rooted but beware...if you break off the stems and leave them in the lawn they will re-root. Creeping charlie sends out runners and it roots all along the stem. I use a "claw-shaped" cultivator that gently lifts the runners and it is easy to pull the plant out.
If this is too much work you can use a non-selective herbicide that is labeled safe for pets and children. The most effective time to apply these herbicides is in the fall.
Here is a link that tells you how to control/eliminate this common weed:
I hope this is helpful. Please contact AaE again if you have further questions.