Maybe the Big Guy–the parent (itself a copy) of 200 children(!)–eats up some render or CPU time because of something you do in a FSM of this Big Guy the moment it receives the event which, for some reason, fires up the 200 children at the same time.
Assuming you have some margin of operation, you might optimize this by sorting the 200 children into several child groups (like 4 groups of 50 each, or 8 x 25, etc. but be careful not to use too many frames) and have the FSM on the Big Guy go through each child group during several frames.
So you're looping through all these child groups one by one, one frame at a time, forcing a pause by using Next Frame Event after processing each child group.
Eventually you might even begin this before the moment you really need the Big Guy, ergo simulating a kind of preloading, so the moment Big Guy and his Big Family are needed, most of the bread is already baked and ready to be served. :-)