If not for the second comma in that sentence, your interpretation might have squeaked by.
There is no comma in the original text. In fact, there aren't even spaces between the words. This comma, as with all other punctuation, was inserted by the translators. Different translators will put commas in different places, depending on their preconcieved beliefs. For example:
11And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;
12For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ (Eph. 4:11-12 KJV)
Notice that there are two commas in verse 12, indicating that the people mentioned in the previous verse are supposed to do all three things - perfect the saints, do works of ministry and edify the body of Christ.
11And He gave some as apostles, and some as prophets, and some as evangelists, and some as pastors and teachers,
12 for the equipping of the saints for the work of service, to the building up of the body of Christ (Eph. 4:11-12 NASB)
Here we have only one comma in verse 12, indicating that the people in verse 11 are supposed to perfect the saints, so that the saints can minister to each other, thereby building up the body of Christ.
See the difference? And it's all because of a single comma - one that isn't in the original text, but was put there by the translators of the KJV. Since a single comma can have such an effect on the meaning, and since there were no commas originally, we have to look to all of Scripture and consider various possible meanings, to find out what the correct understanding is. We cannot base our theology on commas.
It is possible to place the commas differently, and arrive at the following understanding:
After Jesus rose, he appeared to Mary Magdalene on the morning of the first day of the week. (Mark 16:9, my paraphrase)
Since the difference between these two understandings is basically down to a single comma, which was inserted by some translators but not others, we cannot base our understanding on this verse alone. Other verses say the women came while it was still dark or at dawn (which is not the same as sunrise). My understanding of Mark 16:9 does not conflict with these other verses. Your's does, since it has them arriving both before and after sunrise.
I'm going to revise it so that you can see how your mind has been twisting it to say something other than what the syntax is saying in writing.
"After he had risen, He first appeared to Mary Magdalene early on the first day of the week."
See your mistake?
No, but I see yours.
Just for comparison, here's that same verse from some other translations.
Like I said, the translators of different versions interpreted this, as well as many other things, in light of their theology and beliefs they already had, and inserted or ommited commas and other punctuation accordingly. Whatever version you read, you are reading the personal understanding of the translators of that version. That's why it's important to compare versions and look at other possible meanings, whenever there is any doubt.