I've come in late to this but it appears to me that this woman doesn't have enough work to do. If she did she wouldn't be emailing your stakeholders. I have another question, you say there are 5 in the team all at the same grade. Does she carry on like this with the others or is it just you?
5 in the team, but different levels and different work hours. I see her the most. Another team member is having similar issues, but to a lesser extent. She has a good relationship with others in the team.
She should have plenty to do. I think its a personality thing and also wanting to be seen to be doing a good job.
This week has been much much better. Will see how it goes.