Tag trailer hitch

I'd imagine it would reduce the weight of the tongue of the first trailer.....which is SUPPOSE to be a 5th wheel.

You would have to make sure that the receiver on the back of your 5th wheel is capable of using WD. You would also need to check on the strength of the main frame members in the rear of the coach. Many rigs have a very long overhang and the rear frame members are already stressed to the limit or are of a smaller size than the main frame.
I think a lot of the answer to your question would be determined by how much tongue weight is being talked about and how big or long is the utility trailer.

I have seen 5th wheels set up to carry a full dress Harley Davidson on a lift on the rear of a rig. They had to have their frame reinforced from the rear of the rig to all the way in front to the trailer axles. They were parked right next to us for the whole time one winter in Florida. They went out almost every day on that bike and had a blast.:)
Barney

A weight distributing hitch on a truck works by transferring some of the hitch weight from the truck rear wheels to the truck front wheels. So that same hitch on the rear of a 5er would transfer some of the weight from the rear of the 5er to the pin, putting that weight on the truck.

You would want a really strong hitch on the 5er and likewise strongly attached to the frame to accept that levering force it would have to absorb.