Escape the pets

The rules of the game below are as follows:

• The object of the puzzle is to make it to the red square without running into a pet or a pet running into you.
• You and the pets take turns moving.
• You may only move to adjacent squares.
• For every time you move, each cat moves once and each dog moves twice either vertically or horizontally, as indicated.
• When a pet hits a wall, it turns around.
• When you collect a stick, you immediately remove a dog.
• When you collect a yarn ball, you immediately remove a cat.

With optimal play, what is the least number of squares you can move onto (excluding the blue square you're already on) in order to reach the goal?

This problem was inspired by the game Swim Out .