What you have is a clash of expectations. Your group likes to plan and strategize, she clearly doesn't (or rather, planning and strategizing is less important to her than playing this impulsive character). It's really important to articulate the expectations of play and you should do talk to her, and the group, directly, rather than create an NPC to try to block her character.
You'll notice if you look at other media or stories, there's a big difference between impulsive characters who TALK about jumping in, but don't actually do so, vs. those who DO and cause a lot of chaos.
If your group expectations are that everyone is mostly working together and only conflicting/at odds for show ("The elf and the dwarf are arguing again." "Oh, let them be, they're actually good friends.") and she is operating on the idea that each character might have very different agendas or less concern for the group, you're going to have clashes.
Being clear about what kind of game this is, helps her decide if this is the game she wants to play or not.
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.
Best Answer
No, it isn't unfair.
Definitely and explicitly, no. Roleplaying games in general, and DnD in specific, are storytelling games. If you fudge rolls or set up situations to favour one character, that is definitely not unfair on it's own. Fair in DnD and so on is based on making sure everyone gets to;
Roleplay their character
Get an equal or sufficient share of the spotlight time
Not justifiably feel attacked, belittled, insulted or otherwise socially harmed by other players or the GM
If fudging rolls or setting up situations enables those things to happen, it's fine. If it causes those things not to happen, then it's not fine.
In this situation, the following factors are relevant;
the character is a Fighter, one of the least powerful classes in 3e in terms of problem solving
the player has little interest in the rules and is therefore likely unoptimized compared to the rest of the party
'stress relief'; says to me the player is there to kill orcs and be strong, and not to roleplay the intricacies of her character's dead boyfriend and the twilit idylls along the banks of the river shadowheart - ergo the player wants the spotlight time (success, awesome moments, roleplaying) to occur on the battlefield
Based on all that, assuming my assumptions are correct - feel free to fudge dice rolls and set things up specifically for the fighter to smash. Generally if I have a fighter in the group, i'll put things in combat for them to do - orc minions to slaughter, rope bridges to fight across, put the annoying cultist leader somewhere a bit dumb where he can be stabbed to death, etc, etc, because they get so few things to do anywhere else in the game in most editions of DnD, even if the player is a heavy roleplayer and getting spotlight time and fun in other areas.
In this case, shifting things around a bit so her character is more of a God of War than the stats would otherwise indicate seems perfectly fine. Spotlight-stealing is a problem, ruining others' fun or roleplaying is a problem, playing a character doesn't fit into your world (so you feel you have to stop them roleplaying the thing they want to play) is a problem, but fudging dice rolls and letting people win isn't really a problem, just a logistical issue.
Feel free to hammer the other characters still, make them scared for their low hp etc, but if this person wants to not have that, and you have the skill required to give them their victory while making the party feel scared, then you lose nothing by doing it. And potentially gain a bunch of fun, which is the entire point.
Note, when setting up encounters, my typical strategy is to put as many things in there for my players to kill as I think they physically can. Very rarely do I run 'single big monsters', and when I do they are more like a boss monster in a shooting game, a puzzle involving different kinds of attack and movement more than a big pile of hp with a strong attack. My general answer to 'a player wants to kill stuff' is 'have a bunch of stuff that is there specifically to flail and die'.