Hello M.,
I think a lot of this has to do with the single parent thing. I'm one too and I know when I get home Christina has to be with me and have only me do things for her. It's somewhat like separation anxiety.
The only thing that I can tell you to try is to focus her on an activity before heading to another room. Tell her that you are going to do something and be right back. Sometimes if they are reassured that you are coming back in a few moments, the fear is abated. As for the activity, you start her out, then when she's engrossed in it, you quietly get up and walk out. The trick is to try and be back before she finishes :)
Hope this helps a little.
T.