If the father of my child is unwilling to take a paternity test and can not be located can the father's brother take it for him? Will the results hold up in a court of law if they are ever needed?

No, the fathers brother will not show up as the father,
At best it can be "assumed" that a close family member is the father, like the boyfriends father, a uncle and so on.

So no, you need the actual person for the test.