I just got a new Kitten!

I just got a new kitten!  Her name is Minnie, after Minnie Mouse.  She is 4months old, and she has the same exact coloring as Minnie Mouse (All black, white face and white paws).  She is very quiet; much quieter than my Poofy.  Poofy is my Maine Coon Mix or so we think.  But he may even be a Siberian.  Who knows??  I for one, am not about to do a DNA Analysis to find out.... at least not right now.  We are perfectly fine just thinking of him as "Poofy".  He's a big time puff ball.... and a bully so we are learning.
He corners and scares Minnie.  I think he is having an issue with her taking over his space.  He's become quite territorial, and does not want anyone in his Realm.. that being our home.... or his home, where we happen to reside.  Our King, Poofy the King is by far showing his bully side.  I have had to give him several time outs in the bathroom.
And today, for some reason, he has become quite depressed.  He is sitting in a corner and doing a whole lot of thinking by himself.  He barely chases Minnie and he has hid himself behind a set of boxes.  The one time he tried to be a bully, he ran up to her, then just sniffed her and walked away.
She's taken to running the length of the home to tire herself out, with Poofy quietly watching....
Occasionally, he gets into a fit/rage and charges after her.  I'm not sure if its just playful, or if he is really trying to scare or hurt her.  I can't figure cats out.  They are truly a puzzle to me.