Hah, you forget at least one other possible alliance - the one between who is most in the throes of NRE at the moment, which could be either you and the new girl or your wife and the new girl. All in all, things are looking up for your wife
Coming into an established relationship requires healthy respect from the New Girl (or guy). One important thing is to remember that 'If you didn't hear it from them, you didn't hear it from anyone'. People, especially people in NRE, have a tendency to hear what they want to hear. So don't rely on information that has been relayed to your through an intermediary. Although three-way communication can be a wonderful asset in a relationship, especially if somebody involved is a bit shy and has a hard time being upfront about their feelings, it can create a whole host of problems.
Be wary of discussing relationship problems through an intermediary. So, if your wife has issues with New Girl, she should be talking to New Girl about them, not you. If asked, you can act as a facilitator to their conversation, but don't micromanage their relationship and never ever take sides!
Get to know your communication styles. Many people find stuff like the Meyer-Briggs personality inventory or the Five Languages of Love helpful in establishing how they communicate in relationships. Different styles are not better or worse than any other, they are just different. There are bad ways to communicate, too - create awareness for when you or somebody else is trying to manipulate others to want the same things they do instead of communicating about what they need.
Talk about things like who gets to sleep where and how many nights per week. Even silly things, like how much one-on-one sex and in which pairings each member expects to have, as opposed to threesome sex, if threesomes are even going to happen.
Make time for individual dates. Have independent shared hobbies and interests with both. Not every time you talk over Skype or e-mail or text needs to be addressed to everyone.
If in doubt, go Dutch (I mean affection-wise, not financially, although that needs to be talked about too!
). Don't freak out if some connections seem to happen faster and more intense than others - be prepared. Don't fall into playing the 'she got to cuddle you 20 mins and I only 15 last night' games - instead, think of how you could be more giving and how you could support their relationship. If you feel left out, talk about with something like 'I feel left out, I need more cuddling and reassurance' not like 'You are ignoring me, you are not meeting my needs'.
That's for starters, I think. Will add more later if something else comes to my mind.