My heart just sunk when I read "get rid of her" but ultimately that is your decision....so I am going to flood you with ideas in hopes that some will work.
I have a border collie and she is very hyper just like Fairley...the thing I found that has worked the best for us is when she is getting over excited and barking, whinning, pawing when she wants to play, she gets tethered for a quick 30 second time out, if we have to do this 5 times in a row, we do, and then when she is released and is quiet we can then play an appropriate game.
Doing trick training is sooo mentally stimulating it "tires" out her mind and she will most likely be calmer just from that. Tricks that will tire her out learning as well as ones that you can use when she is getting too excited is
-Go to your bed
-Lie down
-Bring me a ball
-Hide and seek
-Find it
-And the usual sit, stay, come, etc.
-We also taught Riley to relax, so when she lies down, when given the command she will fully rest her chin on the ground, in an even more calm position
The relax works well for us when she is barking, because apparently dogs are supposed to find it difficult to bark when they lie down??? Not my girl lol, if she wants to play and is barking and you ask for a lie down, she will lie down and continue to bark, and groan at you. asking for a relax, really calms her down and prevents barking
As for physically tiring Fairley out, combine trick training and self restraint here for him as well. IE. You ask for the ball and he brings it or he just brings you a ball when he wants to play, when you have the ball, ask for a sit, lie down, or whatever it may be, and wait until he does whatever you want him to do first and then reward him with throwing the ball. This is giving a double whammy of mental and physical exertion! Also it really improves the speed of sitting, and lying down (which my girl would always take her time, and not listen to commands when she was in the "border collie stare" with her favorite toy) also having him be able to break his stare by just asking him for a friendly, playfull command, greatly increases your chances of him listening to you if he is ever giving "the stare" to something dangerous, you know his chances of just listening to you will be better, as at first Riley zoned us out completely!
How old is Fairley, and I just realized I was calling her him before...:S sorry, I'm typing as fast as I think LOL And what type of things is she getting into? Things that could be removed from the area that she is allowed to play in? If so, pack em up and move em higher...she can't mess up what is not there for her to...
Riley loves to swim, and depending on where you live, you may even have the option to do that year round, sadly we dont, but its great to tire her out verrryyy quickly!
Also what do you mean by mouthy, how mouthy? Like playful or like ummm your hurting me Fairley!!! :S :O riley is a mouther a bit as well when she gets over excited, but this is when she gets her time outs until she can play nicely, but we worked on her having a soft mouth so its never hard...
Anyway I have to run, this post probably doesnt make sense..please let me know how its going with your princess!!!