For what it is worth, I also switched labs during my graduate training. I'll be honest, it was initially very tense and not the smoothest transition. I think this is partially because my adviser did not realize I was unhappy (despite that I had mentioned previously what I was unhappy about in a very direct manner), so I think it caught him off-guard. In spite of how tense the process was, things were a lot better for me and my only regret is that I had not gathered the courage to do it sooner. I probably spent a year and a half too long being very unhappy in the situation when I could have made the switch sooner. Once I had fully transitioned to the new lab, my previous adviser and I still managed to have a cordial relationship and I was well-supported by the department in making the switch. A few suggestions (totally based on my own experience, so perhaps not applicable to you or your needs):
(1) Talk to your adviser first before talking to the new mentor. This allows you to discuss your concerns first with the person whose lab you are currently in and who, after you (of course), is most effected by the decision-at least initially. Additionally, it allows you to hear her perspective on the situation (she may even agree with you) and also prevents that individual from perceiving that you went behind her back.
(2) When you bring it up, stay focused on the concrete aspects of why you want to switch. Personally, I would avoid bringing any of the interpersonal dynamics that you have experienced that have made you unhappy in the lab in to the conversation. Stay focused instead on your career goals, and how you see those as perhaps being a better fit in a different lab. Again, just my opinion, but bringing the interpersonal into the conversation with your adviser has the potential to make it more messy and may have the inadvertent effect of making you look bad. Whereas staying focused on your career goals and how this other lab will be a better fit for those keeps things more objective and gives off more of a professional vibe.
(3) As for how to address it with lab mates, I actually asked the former mentor what their preference was for me to address it with my peers in the lab. I offered a few possibilities, and asked what their opinion was on the best way to approach letting them know I was switching labs. For any other side projects that I was working on with my lab mates, I also offered to continue my involvement until they found someone to replace my role. This approach allowed me to maintain pretty solid relationships with everyone in my lab after I left, but I actually had a little bit of a different situation than yours, I loved my lab mates. They were awesome to work with, and were well aware of my frustrations...
Do you have weekly meetings with your adviser? If so, that would be a very natural time to bring up your concerns. If not, I would definitely go about setting up a meeting with her ASAP. As hard as it is, the sooner you discuss the issues and start the ball rolling the better for all involved parties.
Good luck! I know it seems hard now, but at least for me, I was so much better off that the discomfort I went through in making the decision and executing it was really worth it.