Alright, so your model for the vault is incorrect. The bottom arm should NOT push out during takeoff. The bottom arm must be allowed to bend so that your head, shoulders, and check can move through your arms and create the necessary position to initiate a swing. Take a look at this image of Bubka - this is exactly the correct position for the bottom arm post-takeoff. Notice that the left arm is bent with the left hand right over the top of his head.
- Bubka_Take-Off.jpg (45.67 KiB) Viewed 37615 times
Your idea of what you are attempting to do is calling "blocking." When a vaulter takes off with the bottom arm locked out, pushing against the pole, the equal and opposite reaction is that the vaulters arm is also pushing the shoulder back, preventing the shoulders and chest from moving, and preventing a swing.
While it is true that the bottom arm should be as extended as possible BEFORE the pole tip hits the box, as you leave the ground, the left arm must be allowed to bend. There is a "realignment" after this point, where the vaulter makes space with the pole, but you're not there yet.
If you broke a pole recently, I'm guessing you've been trying to push the bottom arm out hard, and then you're driving your hands down as you attempt to swing (usually called rowing). This is what probably caused your pole to break, and it's the wrong way to vault. Rowing, much like blocking, stops the natural swing, prevents the shoulders from moving, and forces pressure down the length of the pole, causing it to unbend prematurely. This is also probably the reason you're having trouble making the pit.
If you're having trouble getting into the pit, drop your grip. The first priority is to make the pit reliably, for the sake of your confidence, and then raise your grip gradually when you blow through. Always focus to keeping the hands up when you vault. The hands and elbows must be over your head while you swing. Narrow your grip slightly so you can get the bottom hand higher before the pole tip hits the box, and so that the bottom hand can move over the head while the shoulders move through.
You might post more videos here so we can get a complete picture of what's going wrong, because the video you provided doesn't look so bad.