It's my understanding that MovieMaker only renders things drawn by your processing application within the 'draw' loop to video. That means you'll need to draw the mouse cursor yourself.

On every frame, just draw something to represent your cursor at the mouse position after you're done drawing everything else you want to draw. Since you are drawing the cursor yourself, you can make it look however you want. You can even make its appearance vary when the mouse is clicked, as below.

Code:

void draw(){
//draw your things

//draw the mouse as a transparent red circle
noStroke();
fill(255,0,0,127);
if( mousePressed ) fill(255,0,0); //solid red when mouse is pressed
ellipse(mouseX,mouseY,10,10);

movieMaker.addFrame();
}