My best guess without a video is you are either blocking out (putting your bottom hand way in front of you at takeoff) or planting off to the side. There are a lot of other causes for this (such as pulling with both hands after takeoff), but these are usually the most common for beginners. First and foremost, you should listen to what your coach has to say because he gets to see you jump every day and will likely know the best fix. Beyond that, if one of the two problems I listed is what's causing your issues, I would suggest focusing on letting your chest press forward to the pole after takeoff. Beginners often try to "push" with their hands by locking out the bottom arm and keeping their body back away from the pole. While this can lead to a bend in the pole and a feeling of using more power, it is actually not the correct way to go about putting energy into the pole. Instead, you want to keep your arms tall, essentially hanging from the pole with your top hand and let your chest and body do all the pushing for you. This creates tremendous energy and sets you up for a powerful swing and vault.
Doing grass drills like running past the pole and jumping over the pole will help teach you to keep your hands tall instead of reaching forward at takeoff. This is where I would start. After you're comfortable with that, straight pole drills from a short run (gripping low and not worrying about bending the pole) are the next step. Focus on keeping your body in line with the pole and keeping your top hand straight and tall. Using a really narrow grip will help you resist the temptation to pull with your bottom hand. On these you should focus on letting your body move towards the pole as the pole moves forward. Try to press forward with the chest and drive knee while keeping your tall takeoff position. Your hips should stay under your body and not move past your chest. You'll likely actually make contact with the pole as it reaches vertical, and this is a good thing. Just try not to make the mistake of leaning back and pressing with your hips, as this is a common mistake. From there, you can move on to stay-backs (essentially jumping without the swing). These are similar to the previous drill, but have a few key additions that will help you improve. First, the grip is higher (and the run can be a step or two longer if necessary) and second, you'll be pressing up with your bottom hand while your chest is pressing forward. The key here is that bottom hand is pressing UP not FORWARD! As you get better at these, you will feel your body naturally want to swing, and after you master the stayback you can add in that swing.
Here's a video of the two runway drills I mentioned.
http://www.youtube.com/watch?v=5UJMM9ciswo the first minute of this video shows what I'm talking about. The first 5 or 6 jumps are those straight pole drills. Notice how tall the vaulter's arms are through the whole jump and how his chest presses forward to meet the pole. Also, see how his drive knee stays forward and his hips stay underneath him. From there, the jumper shows the natural transition to the stayback. While he swings on a lot of these jumps, you can see how he still presses forward with his chest and up with his hands first. This is what you should be shooting for.
In addressing your second topic of pushing not pulling, I am going to suggest the notion that what I posted above will also be the first step in fixing this problem. There are certainly other drills you could do to help, but I think that by focusing on these drills you will see the overall vaulting improvement you are looking for. And again, please make sure that you are deferring to your coach's instructions first as he knows more about you than we do. Hopefully this helps and good luck with your jumping.