I don't see anywhere where MD is being a SS. Her birthday is important to her, but she isn't making any demands of her sister. Only a wish that her sister allow her to decline gracefully from attending her wedding. MD hasn't demanded a date, travel expenses or anything, just, "Please accept that I cannot come for reasons that are important to me."
Add to it that her sister has made 0 effort to maintain the relationship with MD (and possibly vice-versa), I can understand why MD would not want to make a Herculean effort to attend the wedding.
There's family, and there's relatives. I'm wondering if for MD, her sister is less "family" and more "relative".
Personally, for my family, I'd move heaven and earth to help them out, attend special events, celebrate milestones, even if it conflicts with one of my own ó probably because they'd just roll the two together and call it convenient that we could get everyone together.* For relatives, on the other hand, I'd go if it were convenient and at little expense, or if it were important to other family that I be there. Otherwise, I'd send my best wishes and regrets that I couldn't make it.
*At my (good, non-toxic) grandmom's funeral my mom used that as an opportunity to announce my pregnancy (with my permission). Whereas in many circles, that would have been, at best awkward, in this particular circle everyone was glad to hear it because not only did it lighten the mood, but it was so much easier to pass the news around. Everyone was even more thrilled when they learned that my grandmom knew about it before she died, especially since it put her firmly in the lead on the great-grandchild count with the other ladies of her church.