Caroline just to give you some food for thought, You are correct about different species NOT being born if two animals mate. However that is not how evolution works. In the grand scheme of things changes are gradual, small and subtle and can take thousands if not millions of years. It is like watching a baby grow you hardly notice any growing at all on a daily basis then all of a sudden they are adults. Well imagine changes over thousands of years.
The modern domestic dog is descended from wolves and through many generations of selective inbreeding and husbandry they became the dogs we see today rather than copies of its ancestors which did not go through the process of selective breeding. It has been documented that some stray dogs have gone feral and joined packs of wild wolves and mated.
http://www.dog-names.org.uk/history-evolution-dogs.htm
We are related to apes I am sorry to break the bad news but the good news is relationship goes way way back in our family trees. I would explain it like we both have the same ancesters if you can go back far enough a very long time back possibly millions of years but apes evolved one way and our side of the tree evolved in a different way. Our DNA is between 95 and 99% identical. The exact ammount is currently under debate. Think of it this way....imagine looking at two leafs on a tree. Now they are very close together but seem unconnected to each other. To see where they originated you have to follow many different twigs and branches till you see the tree.