It's easy to get confused about using "I" and "me" when you're describing an event that involves another person. It helps to separate the actors. Let me explain by using an example. Which sentence is correct?
The Mister and I will not smash cake in each other’s faces.
OR
The Mister and me will not smash cake in each other’s faces.
source
Try this. Separate each word in the subject into a separate sentence:
The Mister will not smash cake. That sounds right! (And if he does smash cake, my MOH will beat him down.)
I will not smash cake. That sounds right, too.
Me will not smash cake? That's obviously wrong. Unless you’re the Cookie Monster.
Now put them together.
The Mister and I will not smash cake in each other’s faces.
Let’s try one more. When Jack Sparrow suggested a pirate-themed wedding to (he and I) OR (him and me), we said, “Shiver me timbers!”
Again, separate the sentences.
Jack Sparrow suggested pirates to I? Arrrr! That’s wrong.
Jack Sparrow suggested pirates to me. Ahoy! That’s right!
Jack Sparrow suggested pirates to he? Again: Arrrr!
Jack Sparrow suggested pirates to him. Ahoy! You’ve got it!
So:
When Jack Sparrow suggested a pirate-themed wedding to him and me (or to us), we said, “Shiver me timbers!”
Now if you've got a pirate-themed wedding with cake smashing, I don't know what to tell you.

On to the lesson: It’s vs. Its

