I had to do this one for a class assignment last year. But what you need to do is create a base command that gets the selected feature from the feature class (make sure only 1 feature is selected).
Use the ITopologicalOperator4 interface to cut the polygon (you must start an edit session on the workspace) by a polyline. The polyline can be programatically created using the envelope of the selected feature (if it's always a proportion of the selected feature, ex. Split the polygon in half). The ITopologicalOperator Interface will spit out 2 geometries that will be the left and right polygons. Store these as features and insert them into the feature class.
Should be good to go. Obviously you have to do some work with the spatial references, starting and ending edit sessions, etc.
Very doable. Good luck.