Firstly, you should talk to all your players about the issue outside of a session. You can get some personal impressions first with one-on-one conversations, but ultimately the entire group should sit down to discuss the problems. Make sure the discussion is democratic in nature, though. JohnP points this out in a related question: "The group setting can be dangerous, as it can turn into people digging up old grievances or ganging up on a particular person."

During the discussion you should ensure that everyone is on the same page about how they want the game to be played. The same page tool is a useful set of questions that will drive the discussion in the right direction. Just make sure everyone is fully involved in the discussion and are voicing their opinions clearly (no passive-aggressive bs). If your players are open to compromises a consensus should be reached.

Secondly, make sure your friend is not suffering from My Guy syndrome. If the description matches (and it sounds like it does), show her the link privately and let her think about it. It should help her be more aware of her role as a player and hopefully remedy some of the issues.

You also mentioned your player gets upset as a result of your decisions. This related question contains a lot of suggestions for how to handle players that take things personally, ranging from studying your own approach to kicking out the problematic player.

In the end, though, you are the GM. You are the writer of half of the story, the referee on all mechanics, and the leader in the quest for fun. The way you drive your campaign is part of your style and your players should respect it. They need to be aware that your goal is always to increase the enjoyment they collectively get out of your game. A certain level of trust and respect is absolutely necessary. If this is impossible to obtain in your group, then the group as it is cannot function. Kicking out players or stepping down as GM would be the next steps to try.

Because the GM is so special, though, new players often fail to grasp just how complex the GM role can be, and can at times see him as an enemy and spoilsport. A neat "trick" you can use to show your players what being a GM is really about (that also gives you some rest from the responsibility of being a GM) is to have another person in the group be the GM for a few sessions. It doesn't have to (and most often shouldn't) be the same campaign you're running. Instead, it can be a few sessions of an off-shoot campaign. It's fun for the players because they get the chance to try out new (and often times silly) character builds, and the new GM will discover what it feels to have all this responsibility. Once everyone has GM-ed a couple of sessions, you will all have an idea of who's best at it and will work towards keeping that person as GM in the future. There's a chance it might not be you, but in the end it should result in a better experience overall.

Keep in mind that not everyone is fit for GM-ing, or willing to try at all. Don't force players to GM, and if they decide to try, encourage them to design very short adventures (no more than three sessions). They can always expand on them later if they like it, or end them early if they don't. The player that questions your decisions often probably thinks they can do a better job, so they're likely to accept your offer to prove themselves.

One of two things is going to have to happen for your group to operate harmoniously. Someone is going to have change how they behave at the table or someone is going to have to leave.

Here are my recommendations for the former. What you've mentioned are actually two distinct (if possibly related) problems. One is that the player is incredibly defensive and the other is that the player is not into PvP in their games.

I'll start with the latter problem because its the easier one to solve. RPGs are a game of cooperative storytelling. That means that everyone has to buy into the premise for it to work. If the game is strongly built around PC conflict, then first you need to make sure she understands the nature of the game. If, after the explanation, she's still not buying in, it may be better to ask her to leave the group. You could still invite her (or everyone) to play a game that is not PvP oriented.

On the other hand, if this is not a PvP oriented game then it may be better to have a conversation with the group about My Guy Syndrome. Explain that there is almost always another choice that makes sense besides attacking the other PCs and unless both players are into PC conflict, it is probably best not to.

If that doesn't resolve the issue on its own, remember that people can't control their feelings (and its generally unhealthy to try) but if they understand their feelings they can better control how they react to them. So my recommendation would be that the next time she starts displaying passive-aggressive behaviors, wait until she is ready to leave and then (depending on circumstances) either walk her outside or ask her to wait behind and talk to her about how she's feeling. Don't judge it; just "You seemed pretty upset during the game. I'd really like to help you enjoy the game. Would you tell me more about how you were feeling and what made you feel that way?" Whatever you do, don't question how she's feeling. Instead try to understand what she's feeling and why. Once you do, you can start asking questions like, "That sounds very frustrating. However, they're not shutting you down because they don't like you. People need to point out when a solution isn't likely to work because if they don't there are usually consequences. But maybe there's another way we can handle that. If you were in their position, how would you handle that problem?"