Hello,
As the previous poster noted you are that other woman.
You are also everyone else in your dream.
I went to dreammoods.com (dictionary) and found this:

Defecate

To dream that you are defecating on someone, indicates your anger and hostility for that person.

To dream that you are being defecated on, represents feelings of guilt and unworthiness.
You may be suffering from low self-esteem.

*Please see also Bowel Movement or Feces.

Whatever this signifies for you, your dream has distanced you from it
by projecting it to another female and even another race.
To me it seems you reacted very strongly to her action,
waking up screaming.

You may want to read up on dreams and their meanings.
Your local library would be a good place to start if you're so inclined.
Best wishes, Marge

There IS alot going on here...

The whole scene
the Big Apple
the beautiful people
going clubbing
open relationships
speak to me of worldliness and sophistication.

You seem at home and happy with this.
(life of the party) center of attraction.

You have invited this other female to join in the fun.
Still she remains aloof, distant.
You seek contact with her even though it's a bit scary.
You find love for her and go against popular opinion
to be with her. (good for you!)
She asks you to accompany her to the bathroom.
Bathrooms are very private spaces.
They are also a space where cleansing takes place.
Where wastes are eliminated.
Where bodies are washed.
Where make-up is applied.
Where we get ready to meet the world... or ourselves...
a bathroom is a place where
you see yourself naked.

The white female...
How do you view white people in general?
What is it about them that you like?
What is it about them that you don't like?

(You don't mention smelling the feces.
I've only had 3 dreams in which scent was involved
so I'm thinking that may be a good thing.)

Your reaction of screaming is very strong.
Are you angry?
confused?
horrified?

None of us need to know, but you do.
Take time out to be alone with this dream.
Ask questions and listen to yourself for answers.
Try them on.
You'll know by how they fit or feel.

Margie