Maybe you could contact one of the therapists on this forum, to see what they have to say about it.
Every 57 days?!... that's so weird. I can't imagine that the body/brain can be responsible for such a consistent frequency. The only thing I can think of is that 57 days is approximately two ovulation cycles, but that doesn't make sense considering her age. Therefore it makes me think that it has to come from an external trigger too, just like other types of CVS.
With this in mind, don't underestimate how well young children can pick up on their mother's emotions. For example, if the mother gets really tense and worried when day 57 comes up, it is entirely possible that the child senses this and reacts to it. In other words, it might be a frequency that has started after the first two or three bouts, which were presumably 57 days apart, and after that the mere anticipation by the mother keeps it alive. Another possibility is that the child reacts to possible moodswings caused by the hormonal cycle of the mother (she ignores the first cycle and only reacts to the second, learned behavior). Although it all may sound weird, the mother is one of the few things that have been consistently present in her daughter's life. As the mother has tried almost everything, it might be an avenue worth investigating, no matter how weird it may sound.
Anyway, I just hope this mother finds a cure for her daughter, or at least some relief. I don't mean to be a mister smartypants who is trying to solve a puzzle about such a serious condition, so apologies beforehand if you feel that way; I just had a strong hunch and couldn't stop myself from sharing it with you.