Currently, the evidence that Joan Welford was the mother of Ruth Liddell is circumstantial, rather than conclusive. We have the following pieces of evidence
1) D_Unknown_Bullen mentions that Ruth's mother was called Joan
2) The same document says that Joan died 22 Feb 1783.
3) Parish registers confirm the burial of a Joan Liddell in Tynemouth on the 24th Feb 1783
4) There is a documented marriage between a Charles Liddell and a Joan Welford in Gateshead in 1728
5) Ruth Liddell, their daughter, was born in Gateshead
6) Ruth's father is given as Charles Liddell in D_Unknown_Bullen, The Three Dorset Captains
1 and O_Unknown_CharlesBullen_Bio_1
7) As of Nov 2021, the
FamilySearch tree for Ruth also shows her mother as Joan Welford
Footnotes
[1]
The Three Dorset Captains at Trafalgar, AM Broadley & RG Bartelot, 1906