don't "offer" what you think is a fair settlement to the problem. They may have a better idea of what is fair and it may be well above what you are hoping for. Just make sure you follow up with a letter so its in a legal form. If its not in print it doesn't count. Ask them what they are going to do to fix the problem. Let them know your very unhappy and feel very grieved against. All companies know what "grievance" means. A problem that the other party expects some form of compensation for.
If the problem was clerical, and by that I mean if they have your photo due to a previous contest you entered it in, and just mixed up the name by accident, then all they need or will do is give you the proper credit in some way. That is where it gets muddled, could there be any connection to the other contest that you did enter your picture in? If you have that information still it would be a good idea to go over all the small print for that contest.
If the other person did somehow get your photo and use it, the calendar people I am sure, have no liability if they have a signed statement from the people who entered photos in the contest that the calendar pictures came from. So if they do anything for you I would be happy. The person who was in the wrong, if it wasn't a clerical error, is the woman who stole the photo.
I have entered my landscape photos to places, most of the time I have to send 1 photo at a time on a cd. Sometimes I have been able to upload a photo online too. I have often found that by entering a photo, even if I don't get it published, I lose all my rights to the photo. Tha'ts why I am wondering if there is some type of trail from the contest you entered it in and where it turned up. The fact that the other girl has a second photo attributed to her could mean your photo should have had your name as the contributor, and the printers or editor messed it up?
Anyway its a pain and a time waster, but you need to see this through, as a hobby photographer, I often wonder if people use my photos as their own. I give tons of my landscapes away, and I am happy to do so, but I worry about all the photos of mine that are passed around on facebook.