Possibly relating to this family:
Louisa Elizabeth Green b. June quarter 1876, Sunderland (fits with the baptism location and date)
Louisa Elizabeth Green, d. Dec quarter 1876, Hartlepool, age zero
These are slightly longer shots going off the deathplace of Louisa:
Ida Green, d. Jun quarter 1880, Hartlepool, aged 35
Thomas Green d. Sep quarter 1880, Hartlepool, aged 31
In this theory Thomas marries Ida (in Germany?) and brings her with infant Edwin back, they have another child, Louisa, who unfortunately dies young, and then both Thomas and Ida die shortly
http://www.durhamrecordsonline.com - data to confirm this in the cemetery registers
A free search shows that Louisa (1876) Ida (1880) and Thomas Humble (1880) Green were all resident at Sunderland Street when buried. There was also an Edith (b. 1877 d. 1879). There are many other Greens buried in Hartlepool around this time but these are the only ones with address Sunderland Street, suggesting to me that they were likely a single family.
Ah, found Edith's baptism!
https://familysearch.org/pal:/MM9.1.1/NB1F-XVCWhy Thomas is only "Thomas" at death but has his middle name on the burial record I don't know. One of the birth certificates for the girls would give you Ida's maiden name.