Extend functionallity of a class: inheritance or java's dynamic proxy

Currently I have three classes and respective interfaces and respective builders:

• Tree: the data structure (implemented in SimpleTree)
• ProbabilityTree: is a Tree with added functionality to randomly select child nodes and to adjust the probability of selecting a node (implemented in ProbabilityTreeImpl).
• DynamicTree: is a ProbabilityTree which dynamically constructs nodes when a requested node doesn't exist yet.

The client code needs Trees that support both random selection of nodes, as provided by ProbabilityTree, and the tree dynamically growing when yet unexisting nodes are requested, as provided by DynamicTree.

NOTE: Currently all three trees are immutable after having been build; for DynamicTree this means clients cannot add or remove nodes, but the tree itself can automatically change.

NOTE: See Github gist with the five Java classes for the code.

There are at least two issues with this design:

1. DynamicTree is derived from ProbabilityTree, while conceptionally these two capabilities are unrelated (i.e. orthogonal).
2. Using inheritance to add functionally is often considered "bad design" (correct me if I'm wrong here).

An alternative design would be to decouple ProbabilityTree and DynamicTree using something similar to the decorator and/or adapter pattern. Using Java's dynamic Proxy might enable "decorators" that extend the interface and that can decorate other Trees with extended interfaces; i.e.:

TreeDecorator implements InvocationHandler, ... { Tree adapted; ... Object invoke(Method method, Object[] args) { if( «this class can/should handle method» ) { return method.invoke(this, args); } else if ( «this.adapted can/should handle method» ){ return method.invoke(adapted, args); } }; } 

Again there are some issue's:

1. Using Proxy makes the code more difficult to understand.

What shall I do? Use inheritance to extend functionallity, use dynamic proxy, or something else?