I think perhaps you should not concentrate on hoping to find DNA matches with any children, natural or adopted, of Robert and Mary Vincent.
It really does depend upon who has tested and who hasn't, and you may not be able to find anybody suitable to test or who has been tested.
If you focus more on your line and your descent from your grandmother, you may get further.
If you do autosomal DNA testing your focus would be on your grandmother's parents, not her siblings. You look for matches to your Most Recent Common Ancestor or MRCA. You will find matches on your great grandmother's and great grandfather's line, whoever they may be.
If you get matches to the Vincent and Yorke families you know she was not adopted. If you get no matches to that line, you may share matches with another line which could help your searches.
For example, if I did not know who my great grandparents were for any reason, I would have found a second and third cousin as matches, 4 members of the same family as 4th cousins, someone else a shared match with all of us, so 8 people shared matches. It wouldn't have taken me long to find out which line they were all connected to, even if I didn't know which specific family member I was looking at.
That's how adoptees do it, they have no ideas as to their parent's names, but they hope to get parent, half sibling or first cousin matches initially, followed by slightly more distant matches to back the theory up.
My advice, FWIW, would be to have an autosomal DNA test and see what comes up.
Regards Margaret