S.M.
My four year old has this tendency, she seems to go through phases where she gets clingy or anxious when one of us leaves, usually me. Although it may be hard for you, try asking her why she is upset (you may have to do this at a seperate time, when she is calm). Ask her if she is worried or scared or just pretending or just missing you. You may be surprised by what she tells you - don't put words in her mouth but try to help her verbalize her feelings.
I would also make it very clear that she may not scream at you - it's my opinion that that is not genuine emotion, but more an attempt to gain power over you and keep you there. The main problem with that is merely that it escalates the situation and makes her feel worse. Make it clear that you won't be able to kiss her goodbye or good night if she is yelling and if she wants to communicate with you she must be calm. wouldn't actuallly walk away from her but try to find a happy medium so that she doesn't get away with manhandling you and yelling at you.
Then give her a strategy for coping - this is the most important thing at our house. My daughter used to panic when I left the house (to go to the supermarket for instance). We came up with a plan where she was in charge of closing the door behind me and then she would go wave out the front window when I drove by. It empowered her to have something to do other than just be upset and worry. So, try redirecting her. "When Mommy closes the door tonight, you tuck all your animals in and give them kisses and help them go to sleep."
Also, be very clear about where you are going and what you are doing, so she can visualize. Right now, she is like a little baby who is just fixated on the fact that you are gone. Tell her exactly what you are doing and where you will be. "Mommy is so tired, I am going to get a drink and then get right into my bed. Can I have one of your animals to keep me company?"
Don't make a big, big deal out of it (if you get upset, she will be more upset)... but I wouldn't ignore her either! Her feelings are legitimate, just help her deal with them.