I’ve worked in animal welfare for many years (Humane Society) and I can tell you that killing them really isn’t a good option. If they are repeatedly coming into your yard they most likely are doing so for a reason. I would first look for and remove any source of food that you and/or your neighbors might inadvertently be providing like dog/cat food left outside. Or perhaps there is some kind of habitat that is appealing to them…
If you kill these, they will most likely be replaced by others, until you deal with the reason there coming there. In regards to trapping and relocating you might want to check with your state laws, in Washington it is illegal to trap and release wildlife, even if you use a humane trap (live trap).
Also, animal control won’t usually deal with wildlife as they mostly are concerned with domesticated animals. You would probably need to contact Fish & Wildlife or a similar organization (what every your state agency calls themselves)
Hope this helps.