In Inkscape I'm trying to create an object within another larger object. I want the big object to be split in two with a line that bisects the larger object, but not the smaller. Kind of like the Pokemon ball.

Can I split the outer object using Inkscape path-fu?

You should be able to do this in a similar was as I described in your previous post.

1. Draw the big object.
2. Draw the smaller inside object.
3. Make a copy of the smaller inside object.
4. Select one copy and the outer object, Path -> Exclusion (this will delete the selected inner object, which is why we made a copy)
5. Draw a line through where you want the next division to be.
6. Select the line and the outer object
7. Path -> Division