I haven't read any of your previous (2yo) posts, but because I love kids, I wanted to respond.
So she is adopted, and spent some time with foster families before you became her parent? The first few years of a child's life are very important in forming attachments. Her strong attachment to you in such a circumstance speaks to me of her fear of abandonment in this life. It could certainly be compounded by abandonments in past lives, too.
If you meet her needs for attachment now, the needs will be met and fulfilled. If you pull away from her, her need to be attached could suffer and she will always have those unmet needs. I'd advise to do whatever it takes to meet her strong needs now, and work on helping her grow secure in your love.
She's old enough to talk to and explain things to, so use your words to the best effect, reassuring her of your love and *showing* her your love and committment by not forcing separation on her. Three is not too old, it's still a very young child (even if she seems six feet tall by the end of a long day!). '
Meet her needs now and she will cease eventually to be so needy. Refuse to meet her needs and she will find something else to fill that hole in her psyche - detachment, continually looking to relationships to fulfill her needs (looking for love in all the wrong places, you know the song) etc.
She obviously isn't ready to be apart from you if she still cries after two months of preschool.
By the way, my degree is in Child Developement, I was a live-in nanny for a year to a toddler and a special needs preschooler, I am a trained birth & post partum doula and have eight years experience as a preschool teacher and Center Director - so I've seen ALOT of kinds of kids.
Take care of yourself, too. A tired, frustrated, anxiety ridden mother needs some lovin, too!
Good luck and you sound like a very concerned, loving mother!