http://www.electricscotland.com/webclans/atoc/earlofstirling01.pdf see page 40 says Walter was a gent. Usher to the King's son Henry. William is listed as a gent. of the Privy Chamber to Henry. The decree does not explain their relationship but they evidently approached the King together with an idea the King granted.
p 208: Of the marriage of William, Lord Alexander, and Lady Margaret Douglas, were born a son, William, and two daughters, Catherine and Margaret. William, only son of Lord Alexander, was born about the year 1632. He succeeded his grandfather as second Earl of Stirling in February 1640, and died in May of the same year..
p 259 There is an entire chapter on CHAPTER XII. FAMILY OF SIR WALTER ALEXANDER. AMONG those who followed James VI. to England on his accession to the English throne, was Walter Alexander, a scion of the House of Menstry. Walter Alexander was born at Stirling in 1572 (Funeral Certificate, College of Arms). He obtained the office of " gentleman usher, daily waiter," to Prince Henry, (parents not named).
Walter Alexander married, first, Sara Gray, a native of Scotland. Early in November 1605, he married, secondly, Anne Fowles. Anne, second wife of Walter Alexander, was daughter of Alphonsus Fowles of St James's, Westminster, Justice of the Peace.
p 260 On the 10th June 1621, Walter Alexander was, along with William Alexander, eldest son of Sir William Alexander, admitted an honorary burgess of Stirling (Stirling Burgh Kecords).
Following up on Menstry
https://en.wikipedia.org/wiki/Alexanders_of_Menstrie
still looking have to go for a while