You may not share the same DNA with all the descendants of a set of great-great-grandparents (or more removed ancestor)
Not everyone inherits the same DNA “pieces” from a set of common ancestors. There’s only so much “space” in your DNA and different children from the same set of parents get different “pieces” and only half of their DNA from each parent.
There are four descendants of my Neill great-great-grandparents that have had a DNA test done. They all share some DNA with me. They all share DNA with each other. But we don’t all share the same DNA pieces, we don’t all “match” each other, and we have different “shared matches.”