Is it true to say that the genome of trees includes or at least "encapsulates" the genome of mushrooms?
No.  

Evidence: If you go to the TreeGenes site and examine those tree genomes that have been sequenced you won’t find any fungal chromosome sequences. (And vice versa.)

Reason: Although trees and mushrooms may develop symbiotic relationships they are independently viable (at least the trees), and even two organisms that can only survive in a symbiotic relationship have separate nuclei with separate chromosomes. They are distinguishable, so they are distinguished.