See most offices use a database program that list a master name and then dependents. When the mom takes the kids, they list mom as guantor and then link the kids under her with their insurance. The address for the kids would have been yours as that is where they live AND it matched the insurance records.
then later when she herself went in the system probably just assumed the kids address and insurance was the same for the parent. It's a common mistake.
I once got a bill for my ex husbands 2nd wife.
Some systems of course are better than others but they cost TONS of money