Well, there are several things which could be made to fit the theory, but nothing in the least definite!
All I can say for certain is that in 1861 Robert was still alive and living with Jane:
RG9 P. 3744 Fol 68 Pg 8
Albion House, Sherburn
Robert Johnson Head M 49 Coal Miner B. Durham, Pensham
Jane Johnson Wife M 42 B. Durham, Lambton
Mary Johnson Dau 16 B. Durham, Sherburn
Sarah J Johnson Dau 3 B. Hetton
If this is the same Robert - and it certainly seems to be - then :
an Elizabeth Johnson died Q2. 1856 reg. Houghton le Spring
No age known
a Sarah Jane Johnson was reg. Q2. 1858 Houghton, and another Q2 1859.
Either could be this Sara.
I haven't managed to find a Johnson / Carr marriage; there is one in Houghton Q2. 1857 Robert Johnson / Jane Cowell - which maybe Janes maiden name.
I think the Mary Johnson in 1861 is porbably Mary Carr - born Sherburn as was James on the 1971.
All very up in the air, I'm afraid!

Shall I look for Robert b. 1845 in the 1881 ? Or have I confused you enough?