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You need to master both rocket building, and plane building; because making a shuttle is like trying to do both at once and they have very contradicting needs. I'd recommend getting some more experience under your belt before you try to tackle a shuttle design.
If you must persist though, it's an issue of Center of mass vs. Center of thrust. Your shuttle is like a big cancerous lump on the side of the boosters, throwing everything off balance. You need to angle the thrusters to fight this imbalance. However, COM will shift as you burn fuel, it's no easy task.
If you do not follow the same ascent profile (the same angle at the same speed shown)- you tip over. Those design principles however are indeed not exactly beginner material...
Piece o cake.
http://steamcommunity.com/sharedfiles/filedetails/?id=1223080876
http://steamcommunity.com/sharedfiles/filedetails/?id=1224567181
You know you are doing it right when you move east with your nose still straight up, just like the nasa shuttle.
http://steamcommunity.com/sharedfiles/filedetails/?id=1238405267
Want a real boss fight? try this ;)
http://steamcommunity.com/sharedfiles/filedetails/?id=1226110024
http://steamcommunity.com/sharedfiles/filedetails/?id=1226119075
COM/COT relation becomes several times as complex.
Buuuut, lets start at the beginning. Why do you want to do so? Because of the coolness factor?
Or because of re-useability?
There are indeed a lot of things to keep in mind, and things to master. Especially- landing. Preferably non propulsive, like...well, a space shuttle.
Nope. Actually shuttles tent to be less complex and more stable than even SSTO's during re entry. Not to mention the comparison with pods. The very shape of shuttles, no matter if RL or KSP, is usually aimed at such, up to the degree of self stabilizing. I can throw my CRV's into atmo at 45° and go grab a coffee, no autopilot, not even SAS activated, it will end re entry on -10° pitch at about 20km.
Their agility and stability is THE reason why you would want to go for all the hazzle of launching them. Because you get a lot of stuff and expensive equipment safely back down for full recovery. Its generally more easy to land a cargo bay full of science equipment and some crew compartments than the same payload with a pod based design. Once you mastered landing...
They also dont need a heat shield, no praying the ablator is enough...They trade horizontal for vertical velocity and wise versa and that way can extend an interplanetary return re-entry within safe heat margins by a lot. Even to an upper atmosphere cruise that can bring them around more than half the planet without leaving the atmosphere again until they finally go down. No need for a multi pass atmo break for everything up to and including Jool.
TLDR: Dont launch with an asymetric LV. Try a simple design ontop a normal rocket first, and land it safely without engines. Test re entry, experience their capabilities to decide when to use them in the first place. And thats usually kind of "medium weight high return value" cargo. Then proceed from that point onward.
For inspiration maybe take a look at "CRV's" - Crew Return Vehicles, essentially small shuttle systems like ESA's IXV and Hermes or NASA's X-38.
http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2009/12/ariane_5_in_hermes_configuration_1991/9657602-3-eng-GB/Ariane_5_in_Hermes_configuration_1991.jpg
http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2011/06/esa_s_ixv/9644806-3-eng-GB/ESA_s_IXV_large.jpg
Starting space shuttle like with an asymetric LV is merely only about craft design and such can easily be copied from others. But even that wont help you if you dont come down safely. And the knowledge you gather during landing such will help you designing asymetric LV's as well.
Once you come down safely they become addictive for their THEN ease of use and awesome fund efficiency ;)
Just needs a bit of training.
You could also try to put Shuttle on the nose of a large booster, but that will require a lot of wings at bottom too to balance drag which aren't really necessary otherwise. So rather bad idea, but doable.
And then best Shuttles in KSP are just launched from Runway like regular planes, because Kerbin orbit requirements are much lower than on Earth and because there are a few miraculous Jet engines in KSP.
Did you download and install the KER mod?