How do I get rid of a stray cat that keeps injuring my 2 cats and dog? We live in county. TIA

Depending on where you are, you would call Denton County. Denton Animal Shelter is a city shelter, not county

You have to call the county, the animal shelter won't do it unless you're in the city limits. And you have to trap or contain it in some way before they will come out to pick it up.

Call animal control