The only possible I can see in 1851 is married, so I wonder if he married twice.
Although living in Gateshead, the Donaldsons came from the Yorkshire Dales, and the marriage was at Leyburn:
Matthew Jackson to Elizabeth Donaldson Sept qu 1847 Leyburn 24/379
1851 HO107/2402 fol. p.
Swinburn Place, Gateshead, Durham
Joseph Donaldson head m 52 Labourer Yorks Newsham
Jane " wife m 50 " Moulton
Henry " son s 18 Labourer " Spennithorne
Eleonar " dau 13 At home " "
John " son 11 Scholar " "
Thos. " " 7 " " "
James " " 5 " " Preston
Matthew Jackson son.in.law m 28 Labourer Preston
Elizabeth " visitor m 29 "
Ann " " 4 Scholar Spennithorne
The only way to find out is to get the marriage cert for him and Elizabeth Watson, that would also show his father's name and occupation which would help to confirm (or not) the 1841 census, and show if he was widowed.
Barbara