It's hard to know what the true stories were from your childhood, but my feeling is that she would have made contact somehow if she'd really wanted to.
Maybe suggest a date she can come and see her (biological) grandchildren -maybe go somewhere neutral like a playground or something- and tell her that otherwise she needs to run by you any intented visits, or tell her simply that if she wants to be part of her grandchildren's lives, then she has to play by your rules.
{btw, your (emotional/real) mother will understand anything you've done in the past to try to mend bridges with biological mother]