So by positing three different visits by three different Mary Magalenes, not only were there three separate people with the same uncommon name but there would have to be at least two different "Mary the mother of James," and thus two different James who both had a mother named Mary. That's a bit much to swallow.
I can understand your tendency to simply assign this to an error or inter-gospel contradiction. But the details of each of the visits all occur at different times. As I noted, the number of Marys around there was much like you'd find in Latin America where Mary's (Maria's) and Jesus's are extremely common. Thus it could have been very likely since Magdala was not far away that three Mary's happened to come from there.
But putting that aside, let's just say there was an unusual coincidence where there happened to be three Marys could called themselves Mary Magdalene. If all the disciples knew of these three by the same name, then it would be confusing or contradictory as they related their stories just what happened. In that case, so that there would not be confusion among those who knew the three Marys would be to describe in one gospel or the other the visit of each.
Further, each of the women seemed to be attached to a household and the name Magda, Magdalene or Madeline in German means Maid. Thus it is thought that perhaps "Magdalene" was understood as some type of a profession or status per that custom, the details of which were lost.
This is just offered as a possibility that resolves the conflict between the accounts without first presuming the NT Bible writers couldn't coordinate their stories; I prefer to give the writer the benefit of the doubt rather than to speculate with modern bias. The contrast to your position is that if we could go back in a time machine we might find there were dozens of girls called "Mary Magdalene" and it just so happened that three of them were attached to households close to Jesus.
Mary, the mother of James, by the way, is Jesus' own mother. James was the brother of Jesus.
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