Trees have placed a central role in most mythological and theological lore because they symbolize life, nature, and the mystery of time. Trees branch out, they their lifespan is interminable, and they all sprout out of a small seed.
In theology we have the tree of life, and the tree of knowledge among some representations of trees in connection to something other worldly.
In the case of Greek mythology the temple dedicated to Zeus is known as the Alti, which is a disambiguation of the word for "small groves", or bushes.
However, the Oak tree is more widely-known to be one of the symbols of the god Zeus, because it is said that another temple of worship made for Zeus in Dodona had, in its center, an oak tree that would rustle to the voice of Zeus on demand. The oak is also the strongest and longest lasting of trees, one of the ones which provides the most shelter, and often a tree that overshadows all others.
Do you mean Zeus' family tree or the family tree of all of the gods? There are a couple of websites that will probably be easier to follow than an explanation of the whole family tree, I included one below. The website goes over the common greek references seen in the calssrooms rather than the more elongated version noting all of the gods. It's important to note that even though Zeus is the King of all gods, he is not the father of them. However, all the gods are related in some way. Zeus is the sibling of five of the twelve olymian gods and the father of two. All of the gods came from uranus or Gaea, otherwise refered to as the "mother earth."