First: "If he drifts out (usually shoulder first toward the gate or toward other horses, etc), you 'bump the outside rein while you give him a thump in the ribs. The intensity of the thump should match the amount he is deviating from following his nose." The outside rein part kind of confusing, if she is drifting outwards pulling the outside rein, or her nose, towards the outside seems backwards.
The reason you bump with the outside rein is that most horses get to this point by a rider trying to get them more to the inside by pulling on the inside rein. So, the horse just learns to 'over-bend' which helps them push the outside shoulder out and actually makes them drift out. If you lightly bump the outside rein, you help in keeping the outside shoulder where it belongs. You bump with the inside rein if the horse tries to straighten out too much. You don't bump hard enough on that outside rein to actually take the horse's head to the outside.
We all strive to teach a green horse to follow its nose. To do that, we need to perfect shoulder control. A horse does not have to follow its nose but it does have to FOLLOW ITS SHOULDER. So, shoulder control (by preventing over-bending) helps teach a drifting out horse to follow its nose. The outside leg insures that it does. Once the horse is in the correct body position (nose slightly to the inside), you should not EVER pull any more on that inside rein. It has already done what it needs to do. It is up to the rider to use a crop or a spur or a bare heel to make the horse follow that nose.
What I have been doing was tipping her head with one rein while squeezing her forwards because she tries to hang on my hands when she drops her head so much,
This is why you bump them rather than giving them something to lean on. While they are green, giving them 'support' only causes them to turn it into more resistance.
The Yo-Yo thing or any form of a busy, unsteady head is fixed by you bumping them any time there head in NOT where you want it for the maneuver you are trying to perform. If you are trying to go in straight line, then you want the horse's head straight in front it. If you are going in a circle, then you want a slight bend the direction you are going.
As a green horse gets more trained, you need to get more critical of where the horse keeps its head. I call it the 'sweet spot' or the 'sweet zone'. I bump the horse's mouth any time the horse goes above or below the 'sweet spot' and give it relief when it has its head in an acceptable spot. Again, the horse learns from what it does that makes you leave it alone. Again, getting off a horse's head and out of its ribs is the only reward it needs for doing the right thing.