SPOILERS, obviously.
Personally I quickly came to believe that the backstory was the main story. That the arrival of aliens was actually a metaphor for the new life that had arrived for her after those backstory events happened.
I still think I’m correct in my assessment. The learning throughout the movie was a metaphor for processing what happened, and the meaning of it, and how to look at it, and so on.
Also they played with the title a bit, in a way that I think is meaningful. The ships have arrived, sort of. But the arrival just brings more waiting (which is kind of the opposite of arrival, like they haven't really arrived yet). This gets even more explicit in the first scene with the aliens. The main character asks "now what?" as they wait there. And the guy says "now...they arrive". Because they haven't really arrived yet, and we're all still waiting. Could be a metaphor for the difficulty of coming to terms with such a loss of a child. It happened, but it doesn't seem real yet, and/or it hasn't been faced yet.
I have to talk about Shutter Island, so SPOILER WARNING for that movie too:
Do you remember that song? The one called "On the Nature of Daylight"? Among other places, it was also used in Shutter Island. You may remember that in Shutter Island [SPOILERS!], there is a house with a lake close behind it. Just like there is at the start of Arrival. You may also remember that, in Shutter Island, the mother who lives there kills her children. In Arrival, the narrator talks of how memory doesn't work the way she thought it did. And we learn that learning the alien language allows one to see what will happen in the future, and what we thought were memories are actually scenes of the future. So our memory of the music from Shutter Island might accomplish this same thing in the viewer, a prediction of what will happen! Cool, huh? Indeed, in Arrival, not only does the child die, but also the mother knew this would happen and chose to let it happen (perhaps people who experience a loss like this wonder about thought experiments like that sometimes?). I'd even go so far as to wonder: is this a (brilliantly communicated) commentary on the morality of having children or something? It's neat, anyways!