No need to be sorry - I hope - just stay safe! I don't like to sound so negative, just that this sounds like a very unsafe situation. I hope this person that's coming to help the horse is also going to help you & your dad too, to learn how to deal with him effectively *& safely*.
I know it's a common practice, but your dad obviously doesn't get how dangerous it is to put a child(rather than an experienced bronc rider who knows & accepts the risks) on a horse that's *likely* to buck, let alone one that's known for it! And no, just putting you back on, with no thought for the reason for the behaviour, doesn't tend to be effective training either. The horse has already been instantly reinforced for his behaviour, by getting rid of you, so the more you do it, the more 'practice' he's getting at it working for him. If you're going to tackle the problem head-on(which I don't advise) by the horse being ridden before he's ready, you'd better all but guarrantee you can ride out those bucks & not come off.
The better, safer way to do it is to train the horse in such a manner that bucking, being headshy, etc, etc is not all that likely for a start. It sounds like the horse hasn't had strong foundations 'built' to be even ready for saddling, let alone having a child aboard. As the horse already has experience with the effectiveness of bucking, I'd ensure whoever was going to train him for you was aware of this, experienced & willing to 'ride out the bucks' should the need arise.
This may just be the difference in a man's perspective of the world and a woman's, but I have to say I don't see getting bucked off as all that dangerous. Rather, I find that folks who haven't been bucked off a time or two to get rather shaken the first time it happens and often become afraid of the horse. I agree that it is best to train a horse such that he never gives it a try, but some horses just enjoy a good buck occasionally and they grow out of it with time, just like teenagers grow into adults - most of the time. I admit that getting bucked off in my fifties is a bit different than it was when I was twelve, but it still does not worry me too much. I just have more incentive to ride it out now, rather than unload!
One of my fondest memories was when I was nine years old and we had a Welsh/Arab pony, about 12.5 hands or so, that would not ride double. Dad put us in an arena with a sand floor and put my 7 year-old brother in the saddle. I would mount on back and see how long I could hang on. We tried to break that pony to ride double, but never succeeded. I can't tell you how fun that was. I can still see my Dad heehawing on the fence as I went head-over-heels off her rump time after time. Of course, there was my mom cursing my dad all the while as well, but she still let us do it, and I thank her for that. I and all my younger siblings learned to ride on that pony. We all shed many tears when she died years later of colic.
So, I have to think that FarmerMorgan's dad knows full well the dangers of letting a kid ride a horse that bucks. Likely he has more experience with that than either of us. He's probably also aware of the problems that come from over-protecting kids and not letting experience be the teacher.
Keep after it FarmerMorgan. Learn how to train a horse out of bad habits. Learn from experience (both your own and from others) and don't be afraid to "get back on" every time.