The common (presumed) ancestor pair is my Gr Gr Gr Grandfather/Mother, and actual Gr Gr Gr Grandfather/Mother to 4 people with the DNA link, not just 2.
That seems like a pretty sure bet to me, but I would like to find out more from someone more knowledgeable about DNA.
What do you call Gr Gr Gr Grandfather/Mother? 3G? 4G?
In any event, these 4 would be my 4th cousins surely?
Parents
Grandparents
1G great grandparents
2G great great grandparents
3G great great great grandparents
Etc.
In your case, descendants from your 3G grandparents, or great great great grandparents, would be 4th cousins to some degree, so sorry, I misunderstood you (not unusual for me these days, but I did say I didn't fully understand!).
4 descendants of possible 3G grandparents are matches to you, from 2 or more different children. Fairly likely that this is the right conclusion to make, that you are also related to this family.
But if it was me, I would still be looking for confirmatory evidence, exhausting any paper trails that would reach the same conclusion (I know you said that they are sparse, so you have probably done this already). I would also be looking for 5th cousin or further matches and 2nd and 3rd cousin matches from the same lines.
DNA evidence is another clue, but not at this stage confirmation. Since they are all descended from the same couple, by definition they are descended from the same 4G, 5G and 6G etc grandparents. It could be from one of those earlier lines that you are connected.
DNA painter gives the following relationship possibilities.
https://dnapainter.com/tools/sharedcmv464 cMs could be as far back as 6th cousins
32.27%Half 3C 3C1R Half 2C2R 2C3R 23.29%3C Half 2C1R 2C2R Half 1C3R 16.73%4C Half 3C1R 3C2R
14.10%Half 2C 2C1R Half 1C2R 1C3R
13.31%5C2R † 5C3R † 7C † 7C1R † 8C † 6C 6C1R 5C 6C2R 4C1R 5C1R Half 3C2R 4C2R 3C3R 4C3R
0.30%Half GG-Aunt / Uncle 2C Half 1C1R 1C2R Half GG-Niece / Nephew
26 cMs further back still
56.00%6C 6C1R 5C 6C2R 4C1R 5C1R 7C Half 3C2R 4C2R 5C2R 7C1R 3C3R 4C3R 5C3R 8C or more distant
16.60%Half 3C 3C1R Half 2C2R 2C3R
16.60%4C Half 3C1R 3C2R
8.60%3C Half 2C1R 2C2R Half 1C3R
2.20%Half 1C2R † Half 2C 2C1R 1C3R
Regards Margaret