ActionScript 3.0 :: Collision And Reflection - Move X / Y Properties

I'm making a game with a moving avatar (it moves by itself ), his direction is given by a vector which only change when colliding with another object (which I called Mirrors ). So my avatar has a moveX and moveY properties ( sort of vector so ). And by clicking and holding the click to somewhere else, then releasing it, you can trace line (Mirrors) which have properties like start and end coordinates, a normalized vector for them, and a normalized normal vector. When the avatar is colliding with a mirror, its move vector change, to be redirected like with a mirror reflection.

Here are problems : The collision is only check before the avatar move, so if my avatar move 3 pixels by 3 pixels, and if my mirror is like x = 5-10, my avatar x = 1, it will move one time : avatar.x = 4, no collision. second time : avatar.x = 7 : collision, but my avatar is partially "in" the mirror, so weird... To solved it, my avatar only move 1 pixel by 1 pixel..

Second problem, when my avatar come in contact with the "bottom" or "top" of my line (imagine a vertical line), it does some strange things like go through the line and shaking.. I don't know how to manage that, it actually occurs sometimes even if it does hit at the line itself.