Java Game - Breaking Down A Method To Smaller Methods And Where To Call

I have a question about a method I have. In my game, I had a move method to move my player left and right, and originally this method was huge, as it also took care checking collisions and a few other things. I broke it up a bit and put the collisions in their own methods and call them from again another method... Here is an extract which I hope illustrates my point:

private static final double MOVE_SPEED = 0.2;
private static final double MAX_MOVE_SPEED = 3.5;
private static final double STOP_SPEED = 0.18;
private double xPos;
private double yPos;

[Code] .....

Something I thought might be a good idea is to check the direction collision when im doing the calculations for that direction:

if(moveLeft) {
dx -= MOVE_SPEED;
(dx < -MAX_MOVE_SPEED) {
dx = -MAX_MOVE_SPEED;
}
checkLeft();
}

But then I would also need to check it when I'm slowing down the left movement:

if(dx < 0.0) {
dx += STOP_SPEED;
if(dx > 0.0) {
dx = 0.0;
}
checkLeft();
}

Then I thought instead i can check it after both of these steps:

if(moveLeft || dx < 0.0) {
checkLeft();
}

I guess my question is quite general: How much is acceptable to break up a method? How many chains of method calls is acceptable? Is it ok to call the same method from different nearby places?