If cats were kids, I'd now have 4!

I hate cats. Not in a violent, aggressive, sort of way--just in a stay away from me and my house and my yard and my children, sort of way. For about 6 months now, there is this cat that will not go away. We NEVER feed it, we don't even give it love or attention, and yet, he comes back. We try shooing it away, he rolls on his back for us to scratch it. We don't! We try to scare it away, he won't go. Whenever I see S at the window yelling, "uhh-ohh!" I know it is because that dumb cat is hanging outside our door again.He even snuck in the house once over the summer when we had the doors open and I found him at me feet in the laundry room (I prompted yelled at it and it didn't move, but I was able to chase it out of the house--but he was not very quick to leave). Today as we were playing outside like it was May 7, instead of January 7, this cat snuck under the fence and came in for a play date with the kids. I kept trying to scare it off and it would have nothing to do with me. Our friends were over and their 2 year old almost hit it with a bat (unintentionally, of course), and it still stuck around. I announced that I didn't like pets and that is why I didn't have one (hoping the cosmos would hear my announcement and send the cat vibes leading away from my house). But then G's friend JT (not JTT) said, "Jaime, you do have pets...this cat right here." The child thinks this is my pet because everytime he comes over, this cat is sitting on my porch or driveway. Anything, but a cat!! A dog or child I might consider taking in at this point, a mole or ferret I could call extension services about, but a cat is a pet. Just not a pet for our family. Anyway, anyone want to adopt what appears to be a loving, kind, unfixed cat?
Note my children up on the swingset waiting for the cat to leave like it was an escaped tiger!