I like this a lot, but there are a few things that I would change.

Addie, he insisted. I was Addie. might do better as Addie, he insisted, I was Addie. I think that I just like the flow of it better that way.

it’s a short drop I can't tell you why, but I would get rid of the it's. I suppose that it just feels a little more like a poem that way, rather than prose. It's something about following the dashes; I think that if you got rid of the dashes and replaced them with something else, perhaps a semicolon, the it's could stay and I wouldn't object.

In a slightly different direction, I would turn and tincture of sanity. into and a tincture of sanity. or perhaps and the tincture of sanity. Again, it's an issue of how it flows for me - maybe others would disagree.

First, I think the subject matter is fantastic when it becomes apparent at the end of a poem. I love reads like this, when you think you recognize a typical morning that you yourself have lived, think it's just a mundane expression of another, only to be slapped in the face by a cold shower at the end.

I only have a few suggestions but many comments:

He never called me Adeline.
Addie, he insisted. I was Addie.
I didn’t argue.

Morning:
it’s dark. I unhinge myself
from the bed (and him)--
it’s a short drop (I'm almost tempted to suggest the removal of the dashes and substitute 'it's' with 'to' so it would read 'to a short drop' )
before feet light on the carpet
and sink in the twisted polyester. (Do you really need the use of so many "the's" above? Also, I feel it would read much simpler if something like this: before feet sink in twisted polyester. It's straight to the point and loses some unnecessary baggage along the way. Basically it would read something like this:

Morning:
it's dark. I unhinge myself
from bed (and him)
to a short drop
before feet
sink in twisted polyester.)

Four pills before
black coffee
and tincture of sanity. (This initially confused me until the ending clarified it.)

His steps leave imprints
that never rebound. (I love this imagery because it implies a light-footed nature; a catlike approach that sneaks up on you)
His breath is a wisp--

“Addie, the lithium.”

There is so much undertone in the following phrases leading up to the ending that appear within the normal confines of morning, but are really provide subtle yet obvious references to pertinent reasons.

he insisted.
I didn’t argue.
(and him)
tincture of sanity
His breath is a wisp--

“Addie, the lithium.”

All of these phrases infer a dominance, a suffocation of types. His insistence. Her willingness not to argue. Unhinging from him as though she were constantly attached. The tincture of sanity could imply a moment of solitude and silence. His breath, the chosen adjective 'wisp' (as compared to bellow), seems to contradict all other subtle innuendos of dominance but in fact is a typical behavior of dominant men. (Ever seen Sleeping with the Enemy where the husband tells the wife, "It's okay. We all make mistakes from time to time?" in a very whispery tone of voice behind her?)

Even the reference of polyester (vs. silk or cotton) signifies a fakeness or man made vs. natural material. This could also be a metaphor for the deliberately false appearance of a happy relationship vs. the natural gracefulness of one. Which, could be another indication of a dominant relationship where the weaker party is inwardly unhappy and merely copes by rolling with the punches of day to day life (Ever seen American Beauty?). This brings me to my last point, the medication.

Everything leading up to the end makes me believe that the reason she takes the medication is to cope with the demands of the relationship. There is no reference of an illness, children, a boss, debt or any additional reasons which could contribute to her frame of mind. Only him. One last thing: Morning: its dark. The emphasis on this is heart rendering because she has is just getting started and has the entire day to go...

All in all I thought the brevity of the poem in combination with with the impact it made was remarkable. Each word solidly chosen and each step placed to evoke compassion and a sense of helplessness as you read. Much like watching something horrible happen when you're powerless to intercede.

I'm with Trevor and detest the ratings feature because I simply don't think I'm qualified to dish them out. But, for the sake of compliance I do. This is undoubtedly one of the best pieces I've read on dA to date. I'm going to basically give a 4 across the board because I don't think anything is perfect.

I hope this was helpful in some way.