You're in a tough spot, being drawn into drama between your mothher and your daughter, triangulated:

You can read more about this dynamic here
PERSPECTIVES: Ongoing Relationship Conflict/ Karpman Drama TriangleHowever your mother is (with the BPD traits), you've done a good thing by providing her a safe place in which to receive her treatments.
What your daughter received from her grandmother was hurtful. You want to rescue, perhaps, both of them to keep the peace. You love both of them, and it sounds stressful being put into the middle.
Not all triangulation is bad, necessarily. It can be stressful always being the referee, however. Maybe helping your daughter to be more compassionate on the front end would trigger more resentment. Validating her feelings may be a better approach. We talk on all the boards about validating people with BPD, but we all need validation in order to feel heard.
Communication using validationThis may also help, with your mother as well:
TOOLS: S.E.T. - Support, Empathy and TruthLet me know if you think this info is helpful.
Turkish