garstonite: yes, I saw that baptism and think it's most likely Thomas, I've only seen him give his birthplace as Newcastle but there's no baptism in Newcastle so this makes sense.
As for them being Housekeeper and Servant on the 1911 census, I'm not too sure why they put that, my only guess would be maybe that because he was still technically married they were being secretive about it? Yes I do have the 1921 census for them, they're ''married'' on this one and apparently had 0 children, for people with a previous marriage would they count those children or is it just between the two now married people? Because if it's none between them then it's more likely he's not the father, but if it's all the children they've ever had then they've just lied anyway.
amondg: yes that's another thing putting me off that Joseph was the dad of Thomas (was in the right area for Ellen though), as he was living in West Hartlepool. But then again, so was Mary Elizabeth on the 1891 census I'm not sure why he was born+baptised there, maybe a clue as to where the Dad of Thomas was at the time?
Annoyingly I can't find Joseph Coulson anywhere on the 1901 census which could maybe help, from the electoral rolls I know he was living with his brother David in 1900 and 1901 but on the actual census there is no Joseph listed in the house with David
Thank you Radcliff, will contact the archives soon and see what I can find. Also thanks for the information about a Thomas Cosgrove in the Workhouse, could be him except I didn't think Mary ever went to prison...