Generally speaking, journals should not have any problem with changing the order of authors as long as all the authors agree with this change and the final version of the paper is approved by all of them. Changing the corresponding author should be avoided unless there is a strong reason for doing so. This is because a level of comfort has already developed between the corresponding author and the editor over the earlier email exchanges.
However, if there is a genuine reason for changing the order of authors or the corresponding authors, I don't think the editor will be annoyed, provided you explain the reason clearly. Ultimately what is most important is that each person receives due credit for his/her contribution to the paper. In certain fields, the order of authors reflects the level of contribution each author has made. If, during the revision, the extent of contribution of the authors has changed, this change should reflect in the order of authors.
There is another angle to your problem. If your professor is a co-author on this paper, you will require his/her approval on the final version of the paper. Moreover, you will have to deal with this professor as long as you are in the same institution, so you should sort out this issue amicably and not let it affect your relationship with him/her. The best course of action would be to discuss the authorship issues with your professor and the other co-authors. Share your concerns with them and come to an agreement on the authorship issue. If all the co-authors agree that the changes need to be made, you can write to the editor explaining the reason for the changes. If the reasons are valid, I don’t think the editor will be annoyed.