I agree with Christina about your Facebook. You have lots of control of who can access you there and elsewhere in your life. Use it.

It was normal to want to discover who your birth mother was. You offered a perfectly appropriate way to have that happen, and she rejected letting your adoptive mom be involved . . . someone that she should feel grateful to. So don't let you and/or your mom get sucked into any more drama with this woman. Maybe some years down the line, she may have a change of heart. For now, she just wants to make trouble, so no need to give her that power.