Bagel

The neighbors got a cat.  Jason told me his name was Bagel.  (I found out later that his name is Oliver, but for this story, we'll still call him Bagel because I thought that was a funny name.)  The cat became a serious problem at our house.  Why?  Because we have a dog.  

Every day, Bagel comes to our door and makes a ruckus.  So, Charlie stands at the door and begs to go out.  I let him out and they fight.
The cat is a heat seeking missile aimed for Charlie. Even if I wait until there is no sign of Bagel before I let Charlie out, he suddenly appears. 
 

I used to be able to let Charlie out without a leash, but now, there is no way.  He'd be gone. 
Now, Charlie runs to the end of the leash and the cat comes within inches of him and waits with his paw in strike position, claws out.
Charlie doesn't bark, so the cat doesn't find anything fearsome or scary about him and he just won't leave him alone.

There's no way Charlie is going to do his business if there is a cat waiting to pounce, so bathroom breaks take so much longer than they ever used to take.  It is driving me nuts!

I have tried to let them get acquainted.  I've let them try to roll around and play, but the playing always goes to another level because the cat takes out claws and bites. Charlie thinks they're pals, but he also tries to assert dominance, so they grapple and fight until I pull Charlie away. 
It's super annoying.  I really hope that cat decides to leave him alone soon.  I am going to go crazy.