What recourse does my mother have with grave plot owned by her and deceased husband and children of said husband want to alter grave without her ok?

What does her contract with the cemetary provide?  Presumably, since she is the sole surviving owner, she and she alone has the right to decide what is on the gravesite, but check the contract to make sure.  Assuming that she has full control over the gravesite, she should notify the cemetary that she doesn't want anything further added to the gravesite, that her husband's children are not authorized to do anyting with the grave, and that teh cemetary should check with her before allowing any changes.  If you don't trust the children, perhaps she shoudl also warn the cemetary that any document purporting to authorize changes which bears her signature is likely forged, and that the cemetary should only accept documents either notarized or signed in the cemetary company's presence.