Translation:We are bringing the bottles to the women.
Those examples don't quite work. In your sentences, the trip, Caesar, and school are the sources of the things being brought. Here the women aren't the source of the bottles, they're the destination, hence the confusion. So why do we use the word for "from" when we're bringing the bottles "to" the women?
Further discussion on the difference between portare and prendere - http://sanniti.tripod.com/sitebuildercontent/sitebuilderfiles/portare-prendere_ii.pdf. There is an interesting example there of "prendere qualcuno dall’aeroporto" vs "portare qualcuno all'aeroporto". Ie, when the idea is that you go somewhere to retrieve someone, you use prendere + dalle, whereas if you are taking someone someplace, you use portare + alle. This is a little counter to the current example (portare + dalle), so I'd be very interested to hear what a native Italian speaker has to say about why 'dalle' is used here instead of 'alle'.
Da can be used in 3 situations. 1st. da = "from" as pointed out in the lessons. 2nd. in expressions of time to indicate how long a action has been going on i.e., abito in Italia da due anni = I live in Italy for 2 years. 3rd. when used in front of a name, sir name or profession to indicate to or at a person's place, residence or work place, i.e., vado da Maria = I am going to Maria's. Maria e' dal dottore = Maria is at the doctor's. So it seems that, in this case, it would mean the bottles are being brought to where the women are.
Given that there is no context in such a short statement, I would have thought that the assorted possibilities would all have been factored in as possible correct responses. There seems to be inconsistency with this, as with the question of why some spelling errors are "heart-breaking" and others only justify a warning!
I really don't get this answer... surely "we bring the bottles to the women" should be "portiamo i bottigli alle donne" ... to the women as dalle means from or by. Even if "bring the bottles BY the women" is what is being translated that is really bad English translation.. or at least incredibly American ... "I'm bringing it BY yours tonight" should actually be "I'm bringing it TO your tonight"