He's not feral he's a pet of one of my neighbors. He has a collar with a heart shaped tag and is very cute looking, like he belongs on a packet of cat food. He's just mean and has beaten up my own cats for years. My current pet, and the previous one who passed on from cancer. He's old now, hence why I was able to catch him.
That's even worse. He is getting in through the cat door? Seal the cat door. Your cat isn't going to die from not going outside. In fact, by letting it free roam in the first place, like this cat's dipshit owner, you are dramatically increasing its chances of dying early and horribly. Think about the situation as a third party observer for a second - you've been letting an animal come into your house, piss around, harass your animals, and damage your property and apparently the only way you decided to address it was by blaming the animal for being an animal (and no, as far as I understand it cats do not really form associations that would make punishments effective.) And you are presumably letting your cat just hang out and do whatever as well. I am somewhere between concerned and terrified, in part for the animals in this situation, but mostly on your behalf because your complacency with this situation makes me wonder whether you are exercising a proper level of self care.
I'm not blaming you for allowing the cat door to...exist thus far, because I think the broad pet owner culture is a little bit delusional. Most pet owners are like pedophiles in that they ascribe a much higher level of intelligence and autonomy to their lessers than they actually possess. Imagine if it was as acceptable for everyone to adopt a bunch of toddlers and let them run around the neighborhood unsupervised. Imagine for years living with your neighbor's toddler just randomly breaking into your place through the dedicated toddler-tunnel you have built into your garage to facilitate the toddler-roaming culture, put up with him pissing and shitting all over your playstations, beating up your own toddlers, and like shooting up heroin on whatever else in your living room, and the one time you caught the little shit you decide to blame him for being a toddler and torture him a little in hopes that his toddler-mind will learn from this and sin no more.
Listen, it's not your fault. The culture is just retarded. But I think you should take care of yourself and your cat and I would strongly consider getting rid of the cat door in order to do that.