extremely helpful
Ok, apologies in advance if there are things in here that you are already doing but I'm not the best at explaining things so I've started at the beginning in an attempt to give some kind of structure! This is the way I would work towards getting a horse going more correctly but you may find different techniques and/or exercises work better for you.
First thing is to make sure he is listening and paying attention to you. It sounds very basic but you need to know that he will go forwards straight away from your leg and will also slow or stop when asked. If you address any issues here first then everything will be much easier later on. Consistency is the key. So if he's resisting the rein aid you need to do tons of downwards transitions, ensuring that you release any pressure as soon as he responds. (It's good to be aware of the rest of your body too as often people tense up or brace the back without realising it, causing the horse to hollow and resist.) It may take a while, but once he understands exactly what you want it will make life much easier and you should find him more accepting of the contact. Equally, if he's slow to react to the leg you need to sharpen him up a little - if he doesn't react straight away give a stronger aid and praise him as soon as he responds, even if he shoots off! Have a review of the turning aids too - does he turn when asked and move away from each leg? I hope non of this has sounded patronising but it's amazing how often we forget about the basics - if the horse understands exactly what you want from him at this stage it becomes much easier for you both to move on to the next.
He's probably rushing because he's unbalanced and also because it's much easier to rush off on the forehand than to carry himself properly. Most people assume that because the horse is going too fast they must be going forwards but it's not usually the case. Fast and forward are two very different things - you want impulsion rather than speed. When you feel a horse rushing the first instinct is always to get them to slow down but what you actually need to do is send them properly forwards and ask them to work correctly. The best way to start doing this is to keep your leg quietly on and put the horse onto a circle. You need to channel the energy he is offering instead of letting it all fall out the front end so you'll probably need to increase the contact a little. You may also need to think about 'holding' the horse with your body - I'm not great at explaining this but if you are sat upright and well balanced in the saddle you can use your core muscles and thighs to help softly contain the energy he's giving you. Lots of transitions are good to get the hind end working and doing plenty of turns and lateral movements will encourage the inside hind to step through. Once he's really stepping under with the hind legs his back will come round and you'll find that the head and neck will come down by themselves. You should feel a real difference when this happens, but having someone on the ground to give you an idea of what is happening can be helpful as well.
Initially he's going to find this really hard work so don't expect a lightbulb type moment - you'll get it for a little while and then lose it again, but his muscles will get stronger with time and eventually he'll be able to carry himself with ease. I find short sessions with lots of breaks good at this stage - if you push on when the horse is tired they just get sore and resistant. As an example, when we first started asking one of ours to work properly he would go very nicely for a short time then would start tossing his head or snatching the rein - this was him saying he was tired, so we would ask him to soften again and then reward him by letting him walk and rest for a while. We would ask for a little more in each session and eventually he was strong enough to work properly for the whole time. It's fabulous when they've built up all the right muscles to carry themselves - even out on a hack just trotting on a loose rein you can have the hind end pushing forwards, the back up underneath you and the neck soft and round in front.
In each schooling session you want to work on getting a good rhythm in all paces, having him forwards into the contact and improving his suppleness. You'll want to do tons of transitions and keep him moving around - circles, shallow loops, lots of changes of rein, etc, aiming to move onto lateral work and lengthening and shortening of the paces. Everything you do should be aimed at activating the hind end and getting him working over his back. Polework is great too - start with them just straight on the floor and work up to curves and raised poles.
Some horses just don't want to stretch and I hate seeing people try to wriggle the head down with hands by their knees. (I'm not suggesting you would do this btw!) You will probably find that as he starts to work more correctly this is something he will offer you for himself. Near the end of the session, as long as you're in a good rhythm and feel that he's carrying himself rather than leaning on you, you can start to let the contact out and he should follow it down. It's great when they will do this and once he knows what you want from him you can ask for the same thing at the start of your sessions to help work him in.
Sorry about the massive post. I've tried to be vaguely coherant but I do have a tendancy to ramble on somtimes. I hope there's something of use to you in there somewhere! A good instructor will be a lot of help to you, even if it's only infrequently, just to keep you on the right track.
