Transitioning Items

I am trying to write an extension that provides parent/child items to move in sync between different states, and along the workflows. An example would be if we are moving a parent item from draft into a review state, by means of the “Submit” transition, its child items would:
A. Figure out what current state they are in
B. Figure out what transition needs to be called to get to the correct destination with its parent item.
C. Actually run that transition in the extension so that the child follows along with the parent.

I have been using the IPSContentWs to find owners and dependents for the parent/child relationships, the API call I am using returns a list of PSItemSummary objects.
From there I need to figure out how to access each item in that list, so that I can find the PSState of the object, which is needed for step B. Once that is found, how would I then call that found transition on the object so that it fires off into the correct state.