I have found the following intriguing events:
George Pemberton Burial in Wilmslow, 16 Oct 1684 principal's residence in Wrenbury
Elizabeth Middleton Burial in Wilmslow, 28 Jun 1688 principal's residence in Wrenbury
They took baby George to Wilmslow to baptise him and also to bury him 60 years later? (He seems much too old to be the husband of Sarah Middleton.) That's reasonable. But why did they also bear Elizabeth Middleton 25 miles to bury her?
1. Elizabeth Anyname who married a Middleton
2. George's Pemberton's sister Elizabeth who married a Middleton
3. The spinster daughter of a Middleton
That little exercise seems to under score the relevance of the connection, but t also raises the question: Which family name was the compelling one here: Pemberton or Middleton, or maybe even both? Since George is the male, it is likely that the Pemberton name is the draw to Wilmslow. That seems to give more weight to the maiden name Pemberton for Elizabeth Middleton.