Q:

How to add a polygon within another polygon as opposed to on top of it?

Sorry for the confusing question. I have a shapefile and I need to draw a polygon in the middle of it. I know I can use the "create features" function, but that creates a polygon on top of the first one, whereas I need it to cut into the main polygon and reduce the area of it, rather than being an independent feature sharing the same space. The same way that the "cut polygons" function divides up the original polygon, but I can't always start from an edge.
Does that make sense? It seems like such a simple procedure but I can't find any way to do it.
I've attached an image to help explain. When I select the main polygon, it doesn't highlight the edges of the smaller polygons within it, meaning they're not altering the shape/area of it.

A:

There are several ways to achieve this. 

try topology tools to fix overlapping polygons. Create a 'topology', use 'must not operlap' rule, and then 'error inspector' window to fix them 
give the cut polygon another chance. Use the 'trace' tool to digitize the small polygons out of the large ones. This is same as 'donut-tricks'. 
sometime converting shapefile to coverage and back into shapefile fixes overlapping issues

