Eradicating an Oak Tree from the Peach Tree

One of our peach trees has been infested by an oak tree!

The only thing we know to do about it is to chop out all the new growth.

I actually quite like the leaves on the oak tree, but I think I like the fruit on the peach tree better. :D

You can see in this picture that the oak tree is growing mostly off to one side of the peach tree, but it actually has some shoots coming right up through the middle of the peach tree's trunk:

Canicus (Pronounced Con-EE-cuss - It's Spanish for Marbles) and Midnight, my kittens, had to come see what I was doing. They wanted to hide behind this box though:


Look at this big pile of oak branches I clipped off:

I wish I thought that was the end of that, but somehow I'm afraid the saga will continue as it has for the past few years. Any suggestions for a total annihilation of this tree would be greatly appreciated.