Even if she IS "one of those women" -- and that's possible, some people are high maintenance, your logic that -- "the last thing I want to deal with is walking through the house barefoot (wood floors), having to wipe my feet off to get my shoes on while juggling my 18 month old, her sister, and anything I have to carry. That and having to either keep my shoes by the door which would require me to know which ones I’m wearing for a few seconds of me walking down the hall" -- is pretty lame.
There is no reason you can't put your shoes on right before you leave the house, to be considerate. I have wood floors, and walk around barefoot all the time, and I put my shoes on right before I leave, and I can promise you it's not that terrible. I don't have to wipe my feet off, I guess because my floors are pretty clean most of the time. (Or try slippers, as suggested below.)
Sometimes living in a duplex requires that you be more considerate than you would have to be if you were living in your own home out in the country with no one else around. That's the downside of a duplex. So I think you should do as she requests, and keep relations amicable. If you don't, and things become unpleasant between you, the consequences will be worse than the hassle of not putting your shoes on till the last minute.
I will believe you that she is "one of those women," but I just have to ask, are you sure you're not one of those women too? Yes, you are being unreasonable.