In reply #5, TerriG mentions an article that stated William was widowed 20 years after his marriage. There is an Isabella Parker that died in 1841 that might be worth looking at, or leaving "on the back burner" to check out when you get desperate!
Her death does not appear (that I could find) on FreeBMD, Anc, or FindMyPast civil death records, but it does at the GRO. And if it is her, she was separated from William, whether for health or other reasons, as her abode is given as Frederick Street, Bishop Wearmouth. She died 01 July 1841, so mere weeks after the census, and yet there is no Isabella Parker on that street. There are Isabella Parkers in the area, which appear to be married, but the '41 doesn't give relationships, and a Hill Parker with (assuming) his wife on Frederick St. Most of the Isabella's I tracked on to 1851, but not all, but they would have had to move to Frederick St., then died, in the time frame between 06 Jun (census day) to 01 Jul, date of death.
One street over, on John Street there are is an older William Potts, but that could mean nothing.
I am wondering if she was ill and staying with/near some relatives, then passed away.
Anyways, the newspaper mention states Mrs., so we know she was a married woman:
Newcastle Courant 09 July 1841
Deaths (Bishop Wearmouth)
In Frederick St., on the 1st inst., aged 44, Mrs Isabella Parker.The GRO has a match for a 44 yr old:
PARKER, ISABELLA 44
GRO Reference: 1841 S Quarter in SUNDERLAND UNION Volume 24 Page 171
The Durham Online Parish has the burial record; I don't know if it is just a full index or the actual image, and they charge £1.50
https://www.durhamrecordsonline.com/FindmyPast also has the burial index. Both of them show Frederick St, and age 44, so it is the one from the newspaper.
The biggest problem is that the burial and death record may not hold any information that helps connect her to your Isabella, even if she is your Isabella. If she died in hospital, the informant is probably a staff member.
The age and timing of this death fits well, but location... not so much, although that could explain why they aren't buried together.