Implementing transition for my character picking up an object from the floor

I need to have my 2D character pick up an object from the floor, and lift it above its head, being able to carry it.

I have figured out that setting the object’s transform.parent to my character’s transform achieves the effect of the object becoming fixed to it. Then I adjust its transform.localposition to move it above the character’s head and presto!

The problem is the transition. If I parent the object to my character first, its coordinate frame changes, and it momentarily disappears to who-knows-where. Then I change the coordinates to something near the origin, and the object comes zooming in back to being close to the character.
The sequence of events happens very similarly if I adjust the coordinates first and change the parenting later.

My goal is simply getting the object to move in a straight line at constant speed from its initial position on the floor to a location near my character’s hand.

What’s you guys’ advice on how to implement this?

Thanks in advance.

Anyone?

Wow, I’m overwhelmed.