How do the spells Animate Objects and Shillelagh interact?

I was looking at shillelagh whose description states (emphasis mine):

The wood of a club or quarterstaff you are holding is imbued with nature’s power. For the duration, you can use your spellcasting ability instead of Strength for the attack and damage rolls of melee attacks using that weapon, and the weapon’s damage die becomes a d8. The weapon also becomes magical, if it isn’t already. The spell ends if you cast it again or if you let go of the weapon.

And then looking at animate objects whose description states:

Each target animates and becomes a creature…

And later lists different object stat blocks, including their attacks.

A number of questions came to mind:
Can you use your spellcasting ability for the animated object’s attacks?
Does shillelagh changing the damage die affect the animated object’s statblock?
And also whether or not this is even possible as shillelagh ends when you let go of the weapon (which is now a creature) and the rule on “Moving Around Other Creatures” states:

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

What happens when you cast animate objects on a weapon affected by shillelagh?