Is there a pet friendly weed killer for my back yard?

You can use vinegar or boiling water to ki the weeds, and that won't hurt your pets!

Boiling water is a great nifty trick to get rid of weeds.

Home Improvements store sell pet-friendly weed killers that will not kill the lawn.

I doubt anything is pet friendly to kill weeds unless all of the ingredients are in your kitchen cabinet. If the bottle says ok for human consumption then I would be convinced it is safe for my dogs. I like the idea of vinegar and hot water. The weeds you mention are green and low growers so I would just leave them.

For controlling most bugs I just use Dawn and water in a spray bottle.

Spray them with white vinegar when there are going to be several consecutive hot sunny days.