I can't find a death for David O. Nickerson, but here's Blanch's death. Perhaps David died and she couldn't take care of the children. I have included the information incase someone else is looking for them.
Index to Death Certificates
Name NICKERSON, BLANCH E.
Sex F
Date 1925 | 04 | 20 (Y-M-D)
County QUEENS
Registration 27589
Volume 27
Microfilm F18930

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No records on ELizabeth at all that I can find, but here are the records on her sisters. There was a brother as well.

Child NICKERSON, EFFIE RAY
Sex F
Date of Birth 1881 | 03 | 02 (Y-M-D)
Place HIBERNIA
County QUEENS
Father NICKERSON, DAVID ORISON
Mother BLACK, BLANCHE ESALINE
Code 1881-N-8
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Child SCOTT, BLANCHE ANNIE MAUD
Sex F
Date of Birth 1907 | 08 | 22 (Y-M-D)
Place SUMMER HILL
County QUEENS
Father SCOTT, HARRY WINFIELD
Mother NICKERSON, EFFIE
Code 1907-802749
Microfilm F21588
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Name NICKERSON, EFFIE R.
Married SCOTT, HARRY W.
Date 1902 | 09 | 24 (Y-M-D)
County QUEENS
Parish ----
Number 2985
Reference B4/1902
Microfilm F15914
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Very strange...two birth records for Alice with different middle names:
Child NICKERSON, ALICE BRIGGS
Sex F
Date of Birth 1884 | 06 | 07 (Y-M-D)
Place HIBERNIA
County QUEENS
Father NICKERSON, DAVID O.
Mother BLACK, BLANCHE ESALINE
Code 4-1-119-4279
Microfilm F14884
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Child NICKERSON, ALICE MAUDE
Sex F
Date of Birth 1884 | 06 | 07 (Y-M-D)
Place HIBERNIA
County QUEENS
Father NICKERSON, DAVID ORRISON
Mother BLACK, BLANCHE ESCLINE
Code 1884-N-10
Microfilm F18772
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me LIVINGSTON, JAMES ALFRED
Married NICKERSON, ALICE MAUD
Date 1910 | 09 | 21 (Y-M-D)
County QUEENS
Parish ----
Number 2303
Reference B4/1910
Microfilm F15938
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2nd marriage:
Name WALKER, JOHN THOMAS
Married NICKERSON, ALICE MAUDE *
Date 1936 | 09 | 02 (Y-M-D)
County QUEENS
Parish HAMPSTEAD
Number 5085
Reference B4/1936
Microfilm F20004
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~Lynne