"When they came over we got one of them to take a taste then told them it was one of the cats that hung around. They were frantic and never returned. That really felt good...."
Great story.
We only seem to have squirrel problems with trees during dry spells when they will chew on the bark of maple or oak for a source of water. They will go so far as girdling a good size branch. The answer in this case is a bird bath.
Have any cats with front claws? I am not a cat person, but we have several at our home and then are outside cats with claws and can climb a tree pretty quick when chased by a big neighborhood dog. No problems with rabbits in the garden either.