Why is the red bud tree called the Judas tree?

The story involves both the dogwood tree and the redbud tree, both of which bloom in Spring right around Easter.

The story goes like this:

The dogwood trees came to Jesus after the resurrection, and made a request - Since the wood that was used to crucify our Lord was from the dogwood, they requested that they no longer grow tall enough or strong enough to be used for timber for this purpose.

The Lord agreed, and since that time, the dogwood has grown short in stature, with small limbs, unsuitable to be used in major lumber projects.

Also, because of the request, the Lord also caused beautiful white crosses to bloom on the tree, with a reddish spot of blood in every bloom, and a tiny crown of thorns at the center of the blossom.

The redbud trees came and asked the Lord a favor as well. Since the great traitor Judas Iscariot had hung himself on this tree, they asked the Lord to ensure that never happened again.

The Lord agreed. Henceforth, all redbud trees have grown short in stature, with limbs thin and low to the ground, unsuitable for hangings.

Also, because of the request, the Lord also caused crimson blooms to burst out along the branches like rivulets of blood, to remind one of the blood Christ shed for the sins of the world, and the innocent blood betrayed by Judas. And the leaves henceforth would grow in the shape of hearts, to remind all who look of the endless and boundless love of God for our lost race.

I always understood that the Judas Tree was the Cercis siliquastrum the tree that Judas hanged himself from.