To move the summer grove, first, if you're moving it within the same ranch, make sure that you have an area cleared off to move it to. Then, click the moving icon, hover over the edge of the grove until the area turns a darker green, click, move, and click again. This will move the grove AND the trees.
However, moving to another ranch takes more steps. IF you are moving the grove AND the trees, you need a tree storehouse. Add as many trees as possible to your tree storehouse. Remove all of the trees. Put the summer grove into the warehouse and go to the ranch you want it on. Place the grove, then transfer your trees into the grove.