Professor moving group project member in the middle of the quarter. What to do?
The professor went behind the group's back by speaking to that individual privately and then announcing the move. This looses the moral high ground from the start...

The "best" manner to have approached this would have been for the professor to have met with the whole group and say "One group is now short and you are plus 1, so could you agree on one person to move". I have had to do this with many groups for projects and, if you show the position and let them work it out, it goes much easier.

Perhaps the professor is "new" to dealing with groups, but IMHO this was handled incorrectly and is difficult to sort now.

Meeting her with the whole group may be best, but whatever the final result (ie who gets moved) she may "target" you for showing her up... As an adult and teacher she should recognize her own fault though... But good luck with that -  it does come with experience... I have been dealing with 30+ plus groups of 5 for 20 odd semesters...