She was not a good parent to you and is she a poor role model of a grandparent to your children.
They do not benefit at all from having any sort of contact with her and you yourself maintain a position of no contact with your mother. That stance now needs to be applied to the rest of your family unit.
A percentage of the general population is dysfunctional and/or abusive. That percentage, like everyone else, has children. Then those children grow and have children of their own. The not-so-loving grandparents expect to have a relationship with their grandchildren. The only problem is, they’re not good grandparents.
Many adult children of toxic parents feel torn between their parents’ (and society’s) expectation that grandparents will have access to their grandkids, and their own unfortunate first hand knowledge that their parents are emotionally/physically/sexually abusive, or just plain too difficult to have any kind of healthy relationship with.
The children’s parents may allow the grandparents to begin a relationship with their children, hoping that things will be different this time, that their parents have really changed, and that their children will be emotionally and physically safer than they themselves were.
Unfortunately, this is rarely the case, because most abusive people have mental disorders of one kind or another, and many of these disorders are lifelong and not highly treatable. (Others are lifelong and treatable; however, many people never seek the necessary help.)
The well-intentioned parent ends up feeling mortified for having done more harm than good by hoping things would somehow be different — instead of having a child who simply never knew their grandparents and who was never mistreated, they have an abused child who is now also being torn apart by the grief involved in having to sever a lifelong relationship with the unhealthy people they are very attached to.
You are the adult here and its your job amongst many to protect them from such malign influences like your mother. She's trying to buy their affection as well; such gifts are never sent in such cases without obligation and other conditions attached.