Hi C.,
Neither of my children have been very needy but I have a friend who's son was. So much that she couldn't separate from him even to go to the bathroom at a playdate. She would leave him at the child watch at the Y and they'd come get her out of class bc he would not stop crying....
The only thing I can tell you is that now that he's 2, he has gotten much better. It was really hard for her but she did start leaving him with daddy to go grocery shopping - should mention th first few times the husband called her asking how much longer cos he wouldn't let up. :)
But it has really worked, she continued taking him to the childwatch even if they pulled her out of class... and now she can leave him - not sure if he cries at all anymore.
I could only suggest that you separte yourself from her a bit, leaving her with a safe person - daddy, grandma.... so she begins to learn you are coming back, she is safe without you.... I did this with both of my kids from the beggining, not very often but I can tell you they are not so clingy that its hurting them - sounds like the lack of trust of others in your daughter is hurting her so it is to her benefit to learn that others love her and she is safe ;)