18Watt

Good luck!  I haven't encountered that exact bug yet, but it's been reported and was well-documented.
Found it! Here's a report of the bug I suspect you're experiencing:
 

Moved to KSP2 Gameplay Questions.
@Trihexia, welcome to the KSP Forums!  
In KSP1, you would need to keep your plane within 'physics range' of the falling objects until they came to a full stop on the ground.  I'm not sure what the physics range is in KSP2, of if that even applies anymore.
However, one thing to try would be to drop your pods from a very low altitude.  Then try to keep your large plane as close to the pods as possible until they come to a complete stop on the surface.

A screenshot of the ship upright in the water, during daylight, would be helpful.
The higher you mount the engines, the greater the pitch moment will be, which will try to force your boat to pitch forward.  
Getting boats to float correctly in the water is not easy.  I have used had good luck with using a little fuel (or ore) as ballast, moving the mass forward or aft as needed to trim the balance.  However my best results are always when I manage to get the center of thrust (COT) as close to being inline with the center of mass (COM) as possible.  
The only real limitation you have is that the propeller blades can never touch the water- they'll be destroyed if that happens.  Otherwise, do everything you can to get the engines as close to the water as possible.  Using the shortest propeller blades helps greatly.  (You'll just need more of them..)
I have not tried using batteries as the hull.  In general it is helpful to have as few hull sections as possible.  The game looks at each battery as a separate hull section, which might give undesired results.
Another problem with those high-mounted engines is you are going to have additional forces when you try to turn the boat.  The boat will try to roll outboard of the turn, which will cause the front outboard pontoon to 'dig in' and produce more drag, which will progressively make things worse- eventually the boat will flip.  Again, mounting the engines as low as possible will reduce that as well.
Good luck!

The problem seems to be the COM is too far aft, or the COL is too far forward.  
One suggestion for having less mass it the back:  Does that small shuttle really need 2 engines?  I suspect a single engine would be more than adequate.  In fact, just for doing orbital maneuvers and a de-orbit burn, a single small engine would be more than adequate.  That would help reduce the mass in the rear of the plane.
Another suggestion is either move the wings aft, or add control surfaces at the very back of the plane, which would move the COL aft.
Finally, one reason your COL is so far forward is because the MK2 cockpits and fuselages produce some lift themselves.  That isn't the end of the world, and can usually be compensated for by reducing engine mass at the back, and adding wing area at the back.
If you are not using the COM and COL display tools in the VAB, those are very helpful in evaluating how changes you make affect the relationship between those two values.
 

Pilots need to be in command capsules to control a vessel.  Pilots located in crew containers are not able to control the ship.

Pilots need to be in command capsules to control a vessel.  Pilots located in crew containers are not able to control the ship.

The 'Tab' button should cycle through active vessels.  Once a Kerbal exits a capsule, the game considers them a separate vessel.  You need to change the focus from the active vessel to the Kerbal.  
If the Kerbal is standing near the capsule, try hitting the 'tab' button on your keyboard.
Otherwise, you should be able to select them from the Tracking Station.

That is configurable in the settings.  
Under settings, select the 'Graphics' tab.
The item you want is called 'Orbit Line Fade Reversed'.  Click the radio button to un-select it.  
 

Here’s what works for me:
Open the KSP folder in a finder window. Locate the KSP app.  This is the file you click on to run, and has a Kerbal icon next to it. Drag that app file to the desktop, and drop it on the desktop. Next, drag the file from the desktop back to the folder where KSP is located.  (Right back to where you found it..) Double click the app, it should start just fine now. You only need to do that the first time you run a new download of KSP, after doing that procedure once you won’t need to do it again.  I have no idea why this works.

I’ll start with the basic- did you set the parking brake?  If you’re not sure, to set the parking brake, you need to click on the brake indicator at the top of the screen.  Hitting ‘B’ applies the brakes only while the button is held.  You want the brakes to stay on even when the Kerbal gets out.
Edit- the rover wheels in your screenshot are retractable….  The parking brake should work, but if not….   

Ore concentrations are not distributed the same in every save, they are randomly generated for each game.  So the location one player reports having high ore concentration may be different in your game- and likely is indeed different.
One tip I would suggest is that the ‘shores’ biome often has a much different ore concentration than the biome slightly inland from the ‘shores’.  So if you are on the shore, and not finding any ore, try moving inland until the biome changes.  Sometimes you don’t need to move very far inland for the biome to change, and the ore concentration to be vastly different.

There is i difference between setting a body as a target, and setting it as your focus.   What you want to do is focus your view on that body.  There are a few ways to do that, I’ll use Mun as an example.
One way is to cycle through all the celestial bodies using the TAB key.  This works, but takes a long time. If you Right-Click on Mun, you should see an option to ‘focus’ your view on Mun.  Again, you don’t need to set it as a target (although you could do that as well), what you want is to set your focus on Mun. There is a keystroke which will reset your focus to the active vessel- I think on most computers this is the tilde key- “~”.  It’s usually up near the ESC key, upper left of keyboard. Also, using the [  ] keys will  cycle your focus among vessels which are near each other.  (I think within ~2.5 km or so). 
 

I was able to make that work, here’s how I did it.
Ship contains a large part in a storage container. Kerbal goes on EVA, has a jet pack but the other inventory slot is open. Position Kerbal near the container with the part. Grab the part.  You won’t be able to add the part to your inventory because it’s too big. But you can add the part to your ship. If you need to place the part a long distance away from the container it was in, you might need to remove and re-place the part, possibly several times, as the Kerbal makes their way to the desired location. I’m not sure if you even need an open inventory slot on the Kerbal to do this, probably not.
There may be other ways to make this work as well, that’s just how I did it.  In my case I was working with the inflatable airlock, and had the same problem, too big to fit in the Kerbal’s pockets.

With ISRU (mining fuel), you can get all the LF and O you need on either Duna or Ike.   I would not bother with high-ISP engines if all you want to do is go between Duna and Ike.  I suspect you will find that frustrating.
Personally, I would use a conventional LFO engine.  I personally like the Vector.  The Vector has a lot of power, and is heavy and expensive.  If you don’t need that much thrust, pick a smaller LFO engine- even Terriers work well on Duna.
Your description is too vague to give a better answer.  Is your shuttle just carrying a single Kerbal in a lawn chair?  If that’s the case, one or two Terriers are probably overkill.  On the other hand, if your shuttle carries 30 Kerbals and a lot of fuel, you need a bigger engine.
Is it possible to use Ion engines?  Probably, but why bother?  In stock KSP all your Xenon needs to be shipped from Kerbin, but you can get all the LFO you need anywhere with ISRU.
I’ve used nuke-powered landers on Ike, but the performance was marginal.  Personally, I wouldn’t bother using nukes on a vessel which only had to go between Duna and Ike.

It sounds like you are just going from orbit to orbit then, and not actually landing your shuttle on either Duna or Ike?   In that case, Ion engines are obviously a workable solution.  However, I still would go for LFO engines, for the same reasons mentioned previously.  

Actually, the plane depicted appears to be a traditional (tail-wheel) design.  In that case, landing front wheels first is recommended.  Or a 3-point landing.  
As bewing said, looks to me like touch down should be around 30 m/s.  I don't think the mass is too much for the gear.  I would be concerned about the long wings, flapping down on landing.  Especially with the engines and fuel located so far from the centerline.
Perhaps try hitting F3 after an unsuccessful landing- it should tell you which parts were destroyed, and in what order.  That may give you a clue as to what is going wrong, by looking at the first few parts to explode.
Actually, taking another look at it, that is a lot of wing for that size plane.  30 m/s may actually be too fast for landing.