Information from Cynthia Glover (nee Coleman), whose great-great-grandfather was William Samuel Allen b.1843. (William's sister, Martha Allen, married Charles Oliver, youngest son of James and Ruth Oliver).

Cynthia writes that Sir Philip married twice:
1. Catherine Hastings
2. Anne Packington, daughter of Sir John Packington

Cynthia writes that Sir Philip and Anne Packington had a son:
1. Alexander Stanhope

Knighthood from, "The History of the Stanhope Family" by Michael Stanhope, 2007. Website as at July 2014:
http://stanhopefamilyhistory.webs.com

Michael writes, “The 1st. Earl Chesterfield married, secondly, Anne Pakington, who had firstly married Sir Humphrey Ferrers. Their only son, Alexander Stanhope, married Catherine Burghill”.

Michael writes of Sir Philip’s first marriage with Catherine, they had fourteen children:
1. John Stanhope
2. Henry Lord Stanhope
3. Charles Stanhope
4. Edward Stanhope
5. William Stanhope
6. Thomas Stanhope
7. Michael Stanhope
8. George Stanhope
9. Ferdinando Stanhope
10. Hon. Philip Stanhope
11. Colonel Michael Stanhope
12. Arthur Stanhope
13. Lady Sarah Stanhope
14. Lady Elizabeth Stanhope

Wikipedia writes, “Philip Stanhope, 1st Earl of Chesterfield (1584 – 12 September 1656) was an English nobleman, aristocrat and royalist, who was created the first Earl of Chesterfield by King Charles I in 1628. Stanhope was the only son of Sir John Stanhope of Shelford, Nottinghamshire by his first wife, Cordell Allington, but was raised by his father's second wife, Catherine Trentham (d.1621). Stanhope was knighted in 1605 by James I. On 7 November 1616, he was created Baron Stanhope of Shelford and was further elevated as Earl of Chesterfield on 4 August 1628".