Hi
Unfortunately I can't find any connection between Elizabeth Winfield, wife of William, living in Mill End, to your Goodman's, or any Goodman's come to that.

Elizabeth Winfield was a Hawkins before she married in 1852, no connection there either, William & Elizabeth are still in Mill End in 1891. There's no mention of her being a "nurse" on the census but I wonder if she could have been someone who sat with dying patients.
The younger Elizabeth you found in Watford doesn't appear to marry & is with her widowed mother in 1901, still in Watford.
Funnily enough the Joseph Goodman who died in India that you mention was one of mine, actually my Uncle's Uncle, they lived in Talbot Road.
To many Goodman's in Ricky..........

If I find anything to help you out I shall be back.
Maddie