John kicked Peter back out = Peter had been outside, then he came inside and then John kicked him outside again (back out)
John kicked Peter out back = John and Peter were outside at the back of a building and John kicked Peter (the normal verb "to kick" in the location "out back")
The only ways I can think to say what you want to say are:
"John got his own back by kicking Peter out."
"John got back at Peter by kicking him out of his store."
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