It looks like you have some work to do with your position and it also looks like pony has some work to do with his technique. He's jumping big and a little inverted, looks like a nervous pony to me! Did you say they the person who tried to train him over fences had the same problems?
You said your dad is horsey, so hopefully he can help you with this: make sure your lunging technique is spot on, poor lunging can create just as many training holes and problems as poor riding can! And then get that pony free jumping, no rider on his back, no hand / leg signals to worry about. Start with ground poles, cross rails, little verticals, etc. until he's super comfortable with it. When you're riding skip the jumping all together and work on poles, create a 'course' of poles on the ground and REALLY focus on keeping your rhythm consistent, pony between your legs and going straight and FORWARD over the poles. Aside from 'courses' I would work on poles on circles (start with circling over 1 pole, and then 2, and then 4), bounce poles and lines of poles. This will help BOTH of you (especially if you really really work on your two-point through all of the exercises).
When you eventually start riding over jumps I'd kick the verticals all together for awhile. I find cross-rails give the pony (and the rider) a middle to focus on. Keep your eyes up, focus on getting to the center of the cross rail, leg on, the same thing you did with the poles. You may also want to try creating a 'chute' to the cross rail (poles on either side of the jump, to keep him from ducking out). Do the same sort of exercises with cross-rails (not verticals), circles, lines, bounce jumps, etc. and when pony is a master at cross-rails you can build it up to some small verticals.
**Normally I wouldn't suggest ANY of that when not working with a trainer, but you said your dad is horsey and I'm hopeful that he's willing to help you out.
Be consistent, but remember not to over-do it. I hate to see people jumping 5 days a week, even small jumps can wear the ponies out and turn them sour.
(The photo is pretty blurry, but I'm going to tell you what I think you should be focusing on in the mean time with your two-point position:
Your legs have swung back, it looks like you're pinching with the knee. Focus on sinking your weight into your heels and supporting yourself with your calves, maybe part of your problem is because you're pinching with your knee, your lower leg is swinging / loose and NOT on ponies' sides telling him to go forward. Keeping your lower leg on and at the girth is a big part of jumping!
In your two-point on the flat work on bringing your tush back over the center of the saddle. As it is you're very far forward over the pommel, bringing your weight back will create a more balanced rider which means a more balanced pony, which will DEFINITELY make jumping easier).
Bring your eyes up! I think this is one of the most important. You're going to go where you're looking, look UP and FORWARD and it'll be easier to get pony to go forward.
I'd like to see you with a little more contact, especially because a problem you've been having is pony ducking out to the side. Have contact with ponies' mouth (not pulling, make sure you know the difference between pulling and contact) and when you do start jumping again plant your hand on the neck and follow his head, bringing your hands up the neck. This way it's harder for pony to duck out the side.
Your very first step is to start working on your position and your ponies' confidence over poles, when you're ready to start working him over fences try free-jumping first. You want to make jumping a good experience every time, while still making sure you're confident enough to catch his mistakes and correct them immediately. It sounds like he's already developed some bad habits, so you're going to have to work pretty hard to correct all of them!