Very interesting.  The family bible lists 8 children and their place of Baptism:  

    (1) June  1908 - St. Andrew's, Gargrave (2)  March  1910 - Broughton (name of church unknown) (3) July , 1912 - St. Oswald's, Thornton in Craven (4)  June  1914 - St. Oswald's again (5) June  1916 - St. Oswald's again  (6)  August 1918 - Earby (7)  November 1921 - Earby  (8)  March 1923 - Earby.   I typed St. Oswald's Thornton in Craven and a picture came up without a name (Yahoo, I think)  strange.  Will look into Fence End some more.  Anyone able to figure out what church in the area was St. Oswald's please go ahead.......the Mystery Church.  Thanks  Stanley.   

Here is what I dug up.  Not all that useful but it might give you a clue as to Broughton.

St Oswald church.

King Oswald of Northumbria was known as St Oswald but should not be confused with the St Oswald who was Archbishop of York in the 10th C.

OS ref. SE0391.Castle Bolton has dominated the skyline of Wensleydale for over six hundred years. Now floodlit in the evening, it is prominent both day and night.
Several unpretentious stone cottages line its single street along a green, with a water-trough at one end and the massive ruins at the other. The castle was erected by the first Lord, Sir Richard Scrope, Chancellor of England, in 1379, it took 18 years to complete.
Designed with a huge, five-storey tower at each corner, their four ranges of living quarters enclose a courtyard, and turrets at two of the sides.
From July 1568 until January 1569 Mary, Queen of Scots, was imprisoned at Castle Bolton in some degree of comfort, with about twenty servants billeted in the village. She is thought to have occupied a large room in the south-west tower, with a fireplace, and steps leading to her bedroom.
Castle Bolton was a garrison for the Royalists during the Civil War, and besieged by the Parliamentary forces in 1645 eventually surrendering.
St Oswald's Church dates from about 1250, and was clearly built before the castle...as the small sundial in the south wall catches no noonday sun. Each summer the church puts on a display, usually an interpretative exhibition of some aspect of Wensleydale's history or wildlife.
Horton-in-Ribblesdale, North Yorkshire, St Oswald

Arncliffe, St Oswald

Guisley, St Oswald.

BROUGHTON HALL
I thought it might possibly be the chapel at Broughton Hall so I dug it out: The Tempests were Catholic and the chapel is dedicated to The Sacred Heart.. It was used for many years by the nuns of the convent at East Marton.

Was this the pic you found?  It is at Thornton in Lonsdale near Ingleton, North Yorks.