My emotions are broken. I want two different things at once, and they are the opposite. It's hard to live with this when you want someone to be with you and for them to go, and either choice is unwanted when I get one. What is it and can I help it?

I don't know that there is a name for it, but it is not uncommon.

An example would be someone who is in an abusive relationship.  They want the person to leave to end the abuse ... But they want the person to stay, because they love them.

Can you seek some counciling to help you sort through some of your emotions?