Is this really normal behavior for a child?

It's perfectly normal,some kids are just like that. I personally was perfect, my mom took me to work. But my brother was like your toddler. What you have to do it just leave. Don't say goodbye, don't keep coming back, just leave. What happened with my cousin, she was horrible when her parents were there, but once they left she was a angel. Just leave, don't look back. She'll grow out of it.