I rashly posted some time earlier that torsional rigidity was not important in a three wheeler.
Following a hard day's work shifting hardcore in a ropey wheelbarrow and subsequent reflections over a beer or two I now believe I was quite wrong.

The issue was I just could not control the wheelbarrow when loaded it had a mind of it's own with delayed reaction when I attempted to turn corners. Empty it was fine if a bit rattly.

Two loads in and I had enough it had to be sorted. The issue was a flat pack barrow that I had assembled in a rush. One of the screws securing the handle had crushed the return lip on the body allowing considerable slack or in our terms zero torsional rigidity.

Tightening the screw restored normality with spacers washers as a long term solutions.

So what was going on? The three points of suspension were here the wheel meets the ground and my hands gripping the handles. A plane through them is slightly below the c of g of the load.

The resulting inertia was enough to resist turning and twist the frame opposing the turn. When the turn finally started the inertia continued long after the desired end of turn. So initial understeer followed by terminal oversteer.

Goes to show you can't beat hard manual labour for refining the thinking process 😀

Now wether the scaling would affect the comparison with a trike is a moot point. After all you would expect even the worst trike to be significantly stiffer than my wheelbarrow but on the other hand a lot faster , hopefully.

I leave the final decision to you.

Cheers!

Torsional rigidity is not entirely unimportant in three wheelers, as there is a torsional moment created between the hub centre and the tyre contact patch of the single wheel.

Although it sounds like simple lack of steering control was the problem in your case, which is a quite different thing.

I made that same mistake when I built a 3 wheeler. I had to add a lot of stiffening. After a lot of thinking, I realised there are 4 points of contact for force. One on the centre of mass and 3 on the road.

Consider turning in to a fast corner. Centrifugal force is pushing the centre of mass out of the corner. Centripetal force is pushing the single wheel in to the corner. That couple is trying to tip the vehicle over. It pushes the outer wheel on the two wheel axle in to the ground. The solid ground "pushes it up" with an equal and opposite force. The remaining wheel is pushed down due to gravity acting on the centre of mass.

Now visualise it and put a finger or thumb on each of those 4 points. With your left hand, put a finger on the centre of mass and a thumb on the rear wheel. With your right hand put a finger on 1 wheel and a thumb on the other. Now rotate your left hand to "apply" cornering force to the centre of mass but resist skidding with the single wheel. You can see the torque on the frame.

All a bit above my level of understanding but I have a cunning plan that may work. Why not add a 4th wheel?
Sir Baldrick