First, what is the purpose of your Get Child? It seems redundant at the least, because you can specify your gameobject to parent to later without pre-setting it at that time. Also.... it's getting an object called "ball" to use as a parent later? As in... the ball? Or is it an object in the Player you are using as a holder for the ball later, to get the right position or what ever? If this is the case, I suggest you rename it to something like "ball holder", just to not confuse yourself later.
Next; the Ball has the Trigger Event and the Set Parent in the same action. This means before it's even triggering, it's already setting it's parent... and as with the above, to whom is it getting parented to? An object with the name "Ball" and also has the tag "Ball"
The Set Parent should be in the Picked Up state, that way it won't happen until after the trigger event.
Something like this would make more sense to me
PLAYER
* Have an object for your player
* Have an object parented to the player in the hierarchy called 'BallHolder'. Position it where you want the ball to snap to when the player receives it
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BALL
* Have a trigger event in the idle like you already have. It should look for the tag Player and send the event PickUp. It should also Store Collider, and use a logical name like 'PlayerWithBall', or etc, as the gameobject variable name.
* In the Picked Up state, do a Get Child for the game object variable 'PlayerWithBall', and tell it to find the Child Name 'BallHolder' (your holder object in the player). Store the result as a logical name like 'BallHolderVar', or etc
* AFTER the Get Child (top to bottom sequence in an action is the order it does things), do your Set Parent. Choose Use Owner (the ball) for Game Object and choose 'BallHolderVar' as the Parent. If you have the Reset Local Position and Reset Local Rotation on, this will mean it will snap to the center of your object called BallHolder.
When the ball is kicked up, do a Set Parent again and leave the Parent as blank (so it will have no parent). Make sure the set position and rotation is off for that one, or it will go to the center of the scene.