Daisy is a bit hard to pin down (the name Daisy Foster isn't uncommon) but there's a likely looking Red Cross volunteer record in 1913-14 and she's with her parents in St Leonards-on-Sea in the 1920s and early 1930s.
I'll include various records for the family, which helps tie things together somewhat, but you likely have some/all of it already.
I couldn't find any newspaper reference about Daisy's death or funeral but as her death was registered in the same quarter as her father's it must have been quite soon after.
Also, I couldn't find any probate records for either of her parents, which seems a bit odd given Robert's occupation/career. If he had left a will it may have named Daisy and had some more info.
GRO BMD references:1889 Q2 Marriage - Robert John Foster & Ellen Gertrude Gorrill; Ormskirk; 8b; 1157
1935 Q1 Death - Robert John Foster; age 71 (born c1864); Battle; 02b; 82
1946 Q4 Death - Ellen Gertrude Foster; age 81 (born c1865); Folkestone; 05b; 586
1948 Q4 Death - Ellen Gertrude Foster; age 82 (born c1866); Eton; 06a; 324
[It's uncertain, to me at least, which death is Ellen]
1890 Q2 Birth - Robert Douglas Foster (mmn: Gorrill); Selby; 09c; 755
1892 Q4 Birth - Daisy Gertrude Foster (mmn: Gorrill); Selby; 09c; 859
1894 Q3 Birth - John Cecil Gorrill Foster (mmn: Gorrill); Selby; 09c; 804
1896 Q2 Birth - Arthur Darrick Huthersall Foster (mmn: Gorrill); Selby; 09c; 885
1898 Q4 Birth - Geoffrey Basil Goring Foster (mmn: Gorrill); Selby; 09c; 891
1903 Q3 Birth - Kenneth Noel Goring Foster (mmn: Gorrill); Selby; 09c; 999
1899 Q1 Death - Geoffrey Basil Goring Foster; age 0 (born c1899); Selby; 09c; 515
1935 Q1 Death - Daisy Gertrude Foster; age 43 (born c1892); Battle; 02b; 92
Red Cross Volunteer:Name: Daisy Gertrude Foster
Dates: 1917 - 1918
Hospital placements: Huntingdon, Peterborough, Uppingham & Norwich
Rank: VAD [
Voluntary Aid Detachment]
Duties: Nurse probationer
Electoral registers:1921-1923: 15 Albany Road, St Leonard, Hastings Borough
Robert John Foster, Ellen Gertrude Foster, Arthur Derrick Huthersall Foster
1924-1931: 15 Albany Road, St Leonard, Hastings Borough
Robert John Foster, Ellen Gertrude Foster, Arthur Derrick Huthersall Foster, Daisy Gertrude Foster
Electoral registers (absent voters list):1922: 15 Albany Road, St Leonard, Hastings Borough
Arthur Derrick Huthersall Foster - Pilot Officer, RAF
Newspaper items:Hull Daily Mail
19 Aug 1915
Former Selby Officer Wounded
Second-Lieut. Douglas Foster, 6th Battalion Lincolnshire Regiment, son of Mr Robert John Foster, formerly of Portholme House, Selby, now of Peterborough, has been wounded in the fighting with the British Expeditionary Force in France. His regiment formed part of the 33rd Brigade, 11th Division.
Leeds Mercury
17 Aug 1916
Soldiers Of Yorkshire Who Have Fallen
From Other Parts
News has reached Selby that Sec.-Lieut. A D H Foster, second son of Mr Robert Jno. Foster, formerly of Portholme House, Selby, and native of the Abbey town has been admitted to the General Hospital at Calais suffering from severe gunshot wounds.
Bexhill-on-Sea Observer
19 Jan 1935
Deaths
Foster - On January 15th 1935, suddenly at "Hazeley", Ninfield-road, Sidley, Bexhill, Robert John Foster, OBE, son of the late John Foster, of York House, Selby, and also of 15, Albany-road, St Leonards-on-Sea, dearly beloved husband of Ellen Gertrude Foster.
Bexhill-on-Sea Observer
19 Jan 1935
Obituary
Mr R. J. Foster, OBE
The death occurred suddenly, in the early hours of Tuesday, of Mr Robert John Foster, OBE, of "Hazeley", Ninfield-road, Sidley, aged 71.
Mr Foster was a retired company director. He came to live in Bexhill two years ago, from St Leonards. He had previously resided in Peterborough and was a native of Selby, Yorkshire. During the war Mr Foster was engaged with the Board of Agriculture and Fisheries, and
was made an OBE for his services in 1919.
He leaves a widow, two sons and a daughter. Two sons were killed in the war and another died as a boy.
The funeral took place yesterday (Friday). A service was held at All Saints' Church, and the interment followed in the Borough Cemetery. The Rev A S F Maitland officiated.
