Ok I just don't think I was getting the whole gist of what you were saying, I thought when I read the ttitle and the first post it was mostly that you were more concerned with the safety of your birds , which of course you are, but the over population is obviously a problem for you, right,
How old are you? You drive, and can shoot a gun, do you work?
I don't understand your refusing to "spend your own money" to take the cats to the shelter, but if it were me and my problem, because clearly nobody else wants it to be there problem, you should not expect them to get rid of or pay for getting rid of the feral cats. Get a job or do odd jobs for a little bit of extra money and take them yourself, Then you could sleep at night without all the yowling and fighting going on with the cats. There are alot of options, rescues, AC, different org. that might help you to get the population down. Your Dad obviously doesn't have a problem with you using the car to deliver the cats to the shelter, all you have to do is put gas in it and go, it really doesn't seem that hard to me.