Blow out the line using a shop vac. Attach the hose to the exhaust side of the Vac and attach to the pump side of the clogged line and blow it back into the pond.
When you say it's "water plastic pipe" do you mean PVC piping - the white stuff we can see in your filter picture? Or some other kind of pipe? If it's PVC pipe, I would go ahead and snake it - I think you'd be hard pressed to damage that stuff with a snake as you have to cut it with a saw. You can proceed slowly from one end and see how far the snake will go anyway and that might tell you where your clog is. And it might just be enough to break it up and get things moving again. But if it's acrylic tubing or some other kind of flexible plastic line, your dad may have a valid concern.
Your ducks are beautiful by the way, but may be more trouble than they are worth with your bottom drain issues. Hey... another thought just occurred to me - what if you abandon the bottom drain completely and set up an alternate line to the filter from a submerged pump maybe? You would then have access to your pump line if it were to continue to become clogged. Just a thought...
(Does anyone else have problems with their font suddenly becoming much smaller or much larger when you are posting? Happens to me every now and again - weird!)
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