The hiragana gives the reading of the phrase
山花笑天下春
さんかわらうてんかのはる
Sanka warau, tenka no haru
Kōrei (亘令) is the name of the priest (of the Ōbaku zen school) who presumably wrote the scroll. He died in 2014. Sho (書) at the end of that sentence just means "written by". So, "Written by Ōbaku Kōrei".
For the translation of the meaning of the expression, I think yours is as good as it might get. Something about the unconscious or un self-consciousness of the bird singing, and the flowers blooming, being a joyous harbinger of spring.