If you are looking for a physically realistic solution, you started at the
wrong way at all - a Truck will never follow a spline. The rear axis never
follows the front (steering) wheels. Think of a long vehicle turning sharp
around a corner - while the front will pass it, the back will cut the edge!
All I want to say is that you can't expect a physically right simulation of
your trailer with any mathematic model, while your truck doesn't follow
physics at all!
But even if you can fix this - for a full phyisical simulaton you will need
a more detailed mathematical and physical description of truck and trailer.
The center of gravity will play a role as much as the mass of the trailer,
the speed of all components and even the friction of the ground. Think of
movements with high speed, on ice or in empty space!

But lets do a simpler model - at first for the simplest trailer-system: a
two-wheeled trailer pulled by hand.
Build a pole - a triangle, where (A) is the left wheel, (B) the right and
(C) the coupling in your hand. So (AB) is the axis and (M) shall be the
middle of the axis (AB). Then lets pull the coupling (C) to any new
position (P) in the easiest way we coul describe and without hurting
physics:
1. turn the trailer around (M) towards (P) so that the trailer is 'looking'
at (P) (the axis (AB) is orthogonal to the direction (MP))
2. move the trailer straight along (MP) until (C) is at (P)

To follow a given path in a smooth manner, we have to do many steps - turn,
move, turn, move, turn, move... - until we are there. Note that this
movement will look different than doing the same at one step and
interpolating the position!!!

In my thoughts and on paper this seems to result in a nearly realistic
movement - i had no time to try it in a simulation yet.

Once we have a solution for this two-wheeled trailer, a pulling system
(truck and trailer) and even a four-wheeled trailer will be simple: put
some poles together, where every coupling is at the center of the previous
axis.
Every four-wheeled trailer will need a pole (otherwise it can't be pulled
around corners!), so you can simply connect two two-wheeled trailers to get
a four-wheeled.
The truck itself will be a two-pole-system, too, where the first coupling is
a thought one: the point where the driver is aiming at. This point will be
the one following your spline step by step.

What do you think about this model?

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