I agree with Sue about the terms used. I would go a bit further and suggest that you maybe initially mention the relationship and after that use their full names. For example I was initially confused about who was the father and who was the grandfather. So if you say “my grandfather Walter Sanders and my nan Amy Starr” then after that you could go on and say “Walter and Amy were not married” etc etc.
Just to confirm, are you trying to find DNA matches to Walter? You are also looking for documentation to prove relationships?
Did your mother have any siblings? If so, was Walter named as their father as well? I am wondering if your Mum was illegitimate, maybe from a casual relationship, or maybe Walter and Amy married elsewhere and you just haven’t found the marriage certificate yet. If you can’t find them together maybe the relationship was casual, though that does not necessarily prove that was the case.
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Regarding your DNA … did you test with Ancestry, and if so, have you looked at your matches in your mother’s side, as they will be your maternal matches and anyone else who matches with Walter should be there. Maybe use a process of elimination to narrow them down …
Do you have any matches that you are certain are related to Amy? If so, you should be able to look at other matches that you and Amy have in common. Any of the remaining matches who do not match Amy and yourself, should be from Walter’s side of the family.
I would look at the highest matches to see if any have trees, then look for any places and approximate dates which might tally. Don’t worry too much if the surname is not Sanders as matches can easily come down the female line and they usually change their surname upon marriage. You should contact possible Walter matches in case they know something about him.
Of course it is possible that the family lines died out so there are no descendants to take a DNA test, maybe no one from that family has tested, or maybe they are more distantly related and you don’t share much DNA so are not showing up.
I’m not sure how clear that is. I’m sure you will get help from others who know more about it than I do. I just wanted to give you an idea of some starting points.
Good luck
