I have this bully that keeps coming onto my Sims lot and pushes and pokes not only the mother and father, but the kids as well. I have tried to corner him and have my Sim "Fight" but he either runs off too quickly or my Sim goes onto something else.

He's terrorizing my Sim family. They constantly have vision of his face burning. Is there anything I can do with this bully?

Are you sure your sims aren't peering into the telescope during daylight hours? If so, that could be the problem. looking into the telescope during the day makes your sim a peeping tom, so that might be causing your 'bullying' trouble.

I'm not really sure. I almost think this started happening before I purchased the scope. I did notice one of my Sims snickering at him recently during the day, but I figured that they were trying to get back at him.

You could download twojeff's visitor controller, and next time he runs on to your lot you can just pause the game, spawn the controller, and ban him from the lot. That's normally what I do to grumpy Sims, since there's no option to have your Sim neglect to spy when using the telescope during the day.