I can only get into a proper haircutter position, straight out of a Layback and have never tried it on the left (I should really try that!!!).
What I do at home is get against a wall, push my hips forward and get into a nice layback position. Try to look at the opposite wall and have your chest completely flat, so that someone can put a glass of water on it. Making sure that you don't move your back, reach back with your right hand (if you are a righty), flex your right foot and grab under your toes. I.e. your hand should be under your toes and your fingers should touch the bottom of your foot. The rotation of you arm should not actually come from the hand, that will put ALOT of stress on your wrist. It should come from your shoulder. If getting into that position is difficult, you might want to consider some shoulder opening /rotational exercises. Once here rotate your shoulder inward( i.e. toward the wall) and pull your foot to your head. The key to getting into a nice position is maintaining your back as far back as possible, so you have to do as little work as possible with your foot/leg.
As for floor exercises:
Exercises Pigeon Twist, Pigeon Crescent, Half King Pigeon, should help open up both your hips and your shoulders so that you can make the transition a bit easier.
http://www.fitsugar.com/Yoga-Sequence-Tight-Hips-33722457#photo-33775410