1851 census shows Robert and Isabella living at 86 Willington New Row, Durham. The census also includes Elizabeth aged 2 years and records her as their daughter.
Here they are on FamilySearch, Elisabeth Dial, 2, born Berry Edge
https://www.familysearch.org/ark:/61903/1:1:SGJR-5LVIf you can't find a death for Elizabeth, it makes me wonder if she was left with a relative, or adopted.
This may be nothing, but...
1861 in Seaham, Durham (piece 3751 folio 57 page 8 )
Thomas Halliday Head 35 Blacksmith, born Durham Hetton le Hole
Margt Halliday Wife 32 Durham Jarrow
Elizth Halliday Niece 12 Servant Durham Berry Edge
https://www.familysearch.org/ark:/61903/3:1:3QHV-P3NF-C9P4-B(gloomy image)
1871 census in Willington, Durham (piece 4965 folio 123 pages 9 + 10)
Margaret Halliday Head Widow 42 Dressmaker Durham Jarrow
Elizabeth Halliday Niece 22 Dressmaker Durham Berry Edge
William Patterson Nephew 21
https://www.familysearch.org/ark:/61903/1:1:VBZ5-RM1 Margaret here
https://www.familysearch.org/ark:/61903/1:1:VBZ5-RMBMarriage?
Sep 1848 Durham 24 85
Halliday, Thomas
Sharlock, Margaret
Partial transcript
9 July 1848, Lanchester
Her father is Thomas Sharlock
https://www.familysearch.org/ark:/61903/1:1:NJNQ-ZMJThen a marriage indexed at Darlington
June 1874 Darlington 10a 76
James Bainbridge
+
Elizabeth Halliday Dial
Could that be her? I can't see an Elizabeth Halliday Dial otherwise. There are two others with the same GRO ref, but local indexes tell us those two married each other.
After that I've lost the bride!