I can’t be positive, but it sounds like you are expecting USD referencing to work more like Maya referencing, where it pulls in all the contents “below” the spot at which you are referencing, whereas USD referencing, as you see, “remaps” the source-target onto the destination prim.
Since you seem to want all three prims/trees present in the final result, I think you want to make three separate sibling prims, each with a single reference on it. And for structuring hygiene, those three prims should each be a child of a single root prim.
There are resources on the ASWF wiki and many other places that discuss pros/cons of structuring assets and how USD composition arcs can be effectively used - have fun!
–spiff