This is classic separation anxiety. We've had several discussions on it, I'll find them and post links in a minute.

Meanwhile, don't believe that she'll be hard to train because she's part Chihuahua. We've got some Chi owners on the board, and they'll tell you what delightful little dogs they can be! Congratulations on rescuing this baby, you may have some challenges overcoming whatever mysteries are in her past, shyness and fear of people being one, but you and she, together, will succeed, I know!

What's her name?