These people are really strange. First of all, who would get mad at your sweet puppy for "running on their yard" when they have a dog of their own who "runs on their yard"? And why would they be mad about you running outside with your shoes off?
Maybe they are just lonely, or do they have family and friends who visit? A man in my neighborhood loves to complain about me. he probably is just lonely, though. I don't even know what he looks like! He ran the tape out of our answering machine on our visit down south complaining about me.
You should do your best to stay away from them; ignore them, don't listen to them when they complain, and try to keep the puppy and your cats "off" of his yard. Letting your cats run around their yard might not be the best thing to do... they all ready called Animal Control Center for some strange unknown reason! If this does not work, maybe you should call someone to complain about THEM.
I know you might not take advice from an 11 year old girl, but it might just work. Good luck with your grump neighbors.

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People who think they cannot buy love have never bought an animal.