Rob Yeung's Answer:
You're dead right that perception is as good as reality. In fact, perception often trumps reality. However, you recognise that the situation is an important one and that's a great start.
You say that you have made some mistakes and that your female boss has since sandbagged you. I wonder if you have tried to have a one-to-one discussion with this female ex-boss of yours.
Sometimes, when emotions run high, people can bear grudges. But if you take her aside, perhaps out for a lunch or coffee meeting outside of the workplace and have a discussion with her, you can repair the relationship you once had with her.
Often, a sincere apology can be enough to get people on side again. Even if you don't believe you were at fault, apologise for having let her down. Contrition and humility may get a better result than trying to argue with her through logic alone. If you have already tried that, then talk to other stakeholders across the business to get their opinions as to why she may still have an issue with you.
If she is reluctant to meet with you, then suggest to the SVP that you, she, and the SVP meet in a three-way discussion. I think it could be dangerous to have a meeting with the SVP alone – if you do that then she could easily believe that you are playing politics and trying to stab her in the back.
Of course, the other way you can defend your reputation is to ensure that your work is of the highest quality. Make sure you go the extra mile for the foreseeable future – deliver your work on time, communicate problems well ahead of time, involve all of the necessary stakeholders, keep an audit trail of what you have agreed to do, and so on. You have to be squeaky clean in your work to ensure that your ex-boss has no ammunition with which she can cut you down.
In terms of managing your emotions, I suggest planning all of your encounters with your ex-boss, your manager, and the SVP. Prepare bullet points before you go into meetings with any of them so you know what you should say and what you should avoid saying. The more thought you can put into preparing for meetings, the less likely you are to blurt something out that could be used against you.