How to explain a cousin link

[GeoffTurner]

My name is Geoff Turner and I live in Brisbane, Australia. I have been contacted by a cousin who lives in Dorset -- let's call her Kelly.
Ancestry tells us we are Half 3rd cousin 1 x removed or 3rd cousin 2 x removed. She is in her 30s and I am in my 70s so I suspect we would be 2 x removed.
We have four shared matches. The first and second have a common ancestor with me -- my 3 x great grandparents Robert Tilbrook and Millicent (Amelia) Hunnibal/Hanibal/Honeyball.
The third and fourth shared matches do not have a shared ancestor, just common DNA.
Kelly is not aware of any link with Robert Tilbrook and Millicent Hunnibal from the people on her tree.
We have done our best to establish a link between Kelly and the Tilbrooks. Three of the four Tilbrook sons emigrated to South Australia, so that should make things easier. At the moment the best we can guess is that Kelly's ancestor Jessie Underwood (1839-1895) must have had an extramarital affair with the remaining son, Stephen Tilbrook (1821-1898). But she was married to another man, James Slaney, when the child Alma was born, so good luck with proving that. 
Does anyone have any ideas about how we can explain the link between Kelly and I?
Thanks,
Geoff Turner

[Biggles50]

It would help if the actual DNA cM figures are given for the match in question and for the shared matches.

Within Ancestry DNA there is the option to add Pro Tools to the package that you have.  This will enable you to see the actual DNA cM that each shared match not only shares with you but what they share with Kelly.  This in turn can help channel research along specific lines if the matches do actually have accurate trees or enough information to build a tree around them.

If I presume that you and Kelly share 40cM then whilst that is a reasonable amount of DNA that suggests a MRCA of pair of your own Great Great Grandparents. However at this amount you can also find that DNA matches that you may have, they do not share DNA with Kelly but they can be a valid inclusion in the family tree.

To give an example, my Wife has a two DNA matches, one of 36cM and the other 42cM, they are in the same family branch and have a closer 2C relationship with each other than my Wife does with either of them.  My Wife has a 1C2R match who we know personally as he is her Maternal Cousin’s Grandson and he matches the 36cM person but not the 42cM.  Such is the random nature of DNA inheritance.

Good luck.

[GeoffTurner]

Kelly and I share less than 1% shared DNA: 23 cM across 1 segment.
Our shared match shares (with me, I assume) 4% shared DNA: 277 cM across 10 segments.