If I understand your post you may be correct but it is confusing.

1st cousins twice removed have s common grandfather. E.g., I and Nina are 1st cousins with common grandparents; her kids and me are 1st cousins once removed and their kids and me are 1st cousins twice removed. Thus I and those kids have their grandmother's grand parent and my grand parents as the common origin. As life times go it is not that difficult to sort out the lineage.

Just to make things more difficult, my kids and Nina's kids are second cousins and those kids's kids are second cousins once removed from my kids.

Got it?