Hi,
I understand the MAJOR part pretty well. Some kids are just hyper-sensitive to Mom's presence - or lack of. First, it sounds like you're doing a GREAT job being a mom. You clearly love your daughter and are genuinely concerned about her happiness and well-being. Also,I disagree that she has been traumatized by her family members - if it was just one person, possibly, but since this is a "mommy-or-no one" situation, it sounds like good old separation anxiety.
Some things that I think help (sometimes):
1 - Give her plenty of warning that you will be leaving. Maybe 1/2 an hour is enough, maybe a whole day's prep is needed. And make sure you use "times" that a 2yo understands, like "after your nap", "when Daddy gets home from work", "after lunch", stuff like that. For a while, the extra warning will mean extra anxiety, but that's your **opportunity** to talk about what's making her nervous and to remind her of all the fun stuff she can do with her caregiver. In time, that prep time will be internallized, so she can kind of prepare herself for being away from you. So keep your explanations about why you have to be away, and who will watch her, as positive as possible.
2 - Play games about her caregivers. "I love when Daddy plays with me because..." "I love eating at Grandma's because..." Let your daughter fill in the blank. Then file away the info, to be repeated back to her when she turns to you with that anxious face. Help her remind herself about what she loves about her other caregivers.
3 - Part of the tantrums could be due to developing verbal skills. Make sure you label her emotions: scared, nervous, sad, unhappy, worried, angry, frustrated. I know most of us like to keep things positive all the time for our little ones, but they have negative emotions too. Helping them label their feelings seems to help them get control over them. Weird, but true.
4 - Get a good-bye routine established. Get your jacket on, purse and keys in hand. Then one hug, 2 kisses, an "I love you", out the door. A big raspberry on the tummy. Waving goodbye through the window. Blowing kisses. Just do the same sequence each and every time. Kids this age absolutely thrive on routine. And if your daughter is too upset to participate, make sure you still do your half of the blowing kisses or whatever.
5 - When it's time to go, GO. As painful as it is (and BOY do I know!), it is more painful for your child if she senses your worry. Prolonging the good-bye tells the child that she's right to be scared, that bad stuff might happen. If you stay calm, confident, and stick to your goodbye routine, she'll get it eventually.
5 - It's nice to have an "I'm back" routine too.
Things that don't work:
1 - Leaving without warning her ("sneaking out") is likely to fail in the long term. It's convenient and it works sometimes, but it sends her the message that you don't think she's important enough to say good bye to. Also, if you can just disappear like that, how will she know that you will be back?
2 - Also, bribing her not to cry or scream. She's entitled to her emotions, and at 2 1/2 she has almost no control over them. Rewards for good behavior are great, but bribes to prevent bad behavior are a bad idea.
3 - Letting your anger and frustration show. She's already fighting for control over her own emotions. If she sees your emotions are out of control, she'll totally lose it. Mommy has to be calm, calm, calm.
My own 3 1/2yo daughter still struggles with separation anxiety. There are days when I feel like it's my fault. But I really KNOW it's not. Some kids are just super-attached. And it's really rough on you when the other adults in your life just don't get it. Check out separation anxiety on AskDrSears.com. There's lots of good stuff there too. I really hope you find something that helps you through this.
-K.