The Ending Is Not Ambiguous (spoiler)
I've seen some comments where people are thinking that Kate and Charlie may get back together. I think we all hope for this to happen, but it won't. Kate still cares for Charlie, but she knows she can't relapse, and that means she has to remove herself from the relationship. The final scene was emotionally tough - Kate wants to support Charlie if he decides to become sober, but she can't force it and it still wouldn't make her comfortable getting back together - she can't compromise her sobriety.
Even sadder, though, and the main reason they won't reconcile, is that their love was built on alcoholism. Kate knows that a sober Kate and Charlie won't have the same bond. Through sobriety, they'll be two new people with new beginnings to be had. This is the saddest part, that Kate's sobriety cost her the marriage.