Re your question about children; the answer is that he was not married:Although the bulk of his Estate went to his brother, he did leave small sums to others
'Probate has been granted to his brother, Sir Hugh Bateman Protheroe- Smith, of Falmouth. Subject to legacies of £50 to his sister-in-law Alice Mackay, £25 each to Gertrude Haig and Sydney A. White, and £20 his cousin, Eric Paul, left his property to brother, Sir Hugh Bateman Protheroe Smith '
The Cornishman, Thursday 16th December, transcribed from image British Newspaper Archive
Extracts from obituary
:Western Morning News, Saturday November 6th, 1937 (Image British Newspaper Archive)
'His brother, Lieut.-Col. Sir Hugh Bateman Protheroe-Smith, was until recently Chief Constable of Cornwall. Their grandfather, Mr. Tom Smith, was Town Clerk of Bideford for nearly 40 years, and their sister married Mr. C. H. Vivian, of the Downes, near Bideford. There are several memorial tablets relating to the Colville Smith family in Bideford Parish Church. Mr. Tom Smith's eldest son, who became Sir Montague Smith, was an eminent judge; another son was killed in the battle of Navarino'....
'... He had a flat in the magnificent building in Great Queen-street which houses the central organization of Freemasonry in this country, and was unmarried. Called to the Bar in 1889 at the Inner Temple, he never practised. He received the C.V.O. in 1923, and was created Knight in 1925.'
(there is a lot of detail about his career on this obit
Here's his progression in the Freemasons but how much detail do you want?)The dates might be able to be checked in the Freemasonry records on Ancestry..
Entering Freemasonry early in life, he served as W.M. of the Apollo University Lodge, No. 357, Oxford. He joined Phoenix Lodge of Honour and Prudence, No. 331, Truro, and in due course was appointed P.G.S.W. of Cornwall.
GRAND LODGE RANK.
In 1899 he received the appointment of Senior Grand Deacon in Grand Lodge and 2nd Asst. G. Sojr. in Supreme Grand Chapter. The same year he was chosen as Deputy Prov. Grand Master of Cornwall by the late Earl of Mount Edgcumbe on the resignation of the late Sir Charles Brune Graves-Sawle. The year before he had been associated with Mr. Bernard F. Edyvean, A.G.D. of C. of Grand Lodge, in laying the foundation and memorial stones of the Masonic Hall at Camborne. In 1900 he laid the foundation-stone of the Masonic Hall at Calstock, and the same year he dedicated the new Masonic Hall at Camborne. He performed the dedication ceremony of the Calstock Masonic Hall in 1901. and in 1902 was elected secretary of the Royal Masonic Benevolent Institution. This position he filled with great success until his appointment by the Grand Master, the Duke of Connaught, in 1917 as Grand Secretary in succession to Sir Edward Letchworrth, who had resigned after serving a quarter of a century in that office. He was also Grand Scribe E. of the Supreme Grand Chapter of Royal Arch Masons, and since 1935 he had been Grand Supt. for Oxfordshire. He was Second Grand Principal of Cornwall'
Apparently he spent his life representing the Grand Lodge of England all over the World. As a Cornishman he was also 'Prov Grand Master in the Mark Degree', of the Province of Cornwall' and he 'regularly attended meetings' in Devon and Cornwall.
A Local memorial service was to be held in Truro Cathedral on 'Tuesday at 3pm'