If you really don't want to keep a member reference variable to the entity manager, you could pass it as a function parameter to the functions that actually need it.
Another way is to make the entity manager a global variable.
Personally I think the member reference variable approach is fine, it's pretty simple. Passing the manager as a function parameter is more flexible, but you probably don't need it unless you are considering the possibility of using the same tree node on different entity managers . On the other side, you have the global entity manager approach. That's a fine approach if you will only ever use one manager.