cantab

I don't have the mods needed.
If it's on launch, you probably aren't able to get the thrust pointing through the centre of mass. The game's SRBs don't have thrust vectoring so you need to rely even more on the main engines - the real Shuttle boosters have gimballing nozzles. Raising the external tank can help. Look at a side view of NASA's shuttle, such as at http://www.nycaviation.com/2011/07/photos-space-shuttle-atlantis-lifts-off-on-final-mission , and see how the butt of the external tank is well forward of the rear of the shuttle - AND consider that because they used low-density hydrogen and denser oxygen, with the oxygen at the front, the centre of mass is towards the front of the ET too. This all means the main engines don't need to be so angled and don't need to gimbal so much.
If your problems are when gliding or on re-entry. You want centre of lift a bit behind centre of mass, and you want elevons a good distance from centre of mass.
Edit PS: A NASA-style Space Shuttle is one of the hardest things to build in KSP. Expect to do a fair bit of design work to get it flying well.

I've done it several times. It's fairly straightforward, but you do want to be pretty "direct" about it, you can't really spend ages slowly closing in.
Anyone who has captured an asteroid in Kerbin's SOI has done this. (Personally I prefer meeting them in solar orbit.)
My basic approach:
Leave plenty of time to get everything sorted out. You don't want to miss the target! If possible, launch to match inclinations. Make a manoeuvre to put your apoapsis touching the flyby periapsis of the target. If this is not possible due to inclination, just put the apoapsis pretty high but closer than the flyby periapsis. At apoapsis, burn to both match inclinations and so that when you reach your intersection with the target trajectory in future you will get a close encounter. You'll probably be going round at least once in quite a high slow orbit, which is why I said you need plenty of time. When you get your close encounter, match speeds then close in as normal. If you wanna get back to the body you were orbiting, do whatever needs doing (docking components, transferring Kerbals, etc) pretty quickly then burn retrograde already. If you are short on time, then an alternative approach is to delay step 3, waiting in a quick low orbit until you can arrange a single burn to a direct encounter at step 4. But you will need a bigger burn to match speeds and it's a bit trickier to sort out the timing.
Here is a trajectory example. My ship was in an equatorial medium Kerbin orbit and needed to rendezvous with the cyan-trajectoried vessel flying through on a high inclination beyond the Mun. One burn to raise apoapsis, a second burn to match inclinations and set up a close encounter. "Close" was actually a few hundred km, though I refined it to 22 km - you have a lot more tolerance in high orbits than you do in LKO because the wider and slower orbits mean you can spend longer on the final straight-line approach.
(The cyan, by the way, was an asteroid I had already met in solar orbit and course corrected so it got a Kerbin gravity assist to a Duna encounter, and I sent some more stuff to meet the asteroid and go along for the ride. A complex and fun mission.)
 
And another situation I had to deal with, this time the craft on the flyby was actually coming closer than my current orbit. I don't recall my exact rendezvous approach, but I think I would have entered a highly elliptical orbit then met the target at our shared periapsis instead of at my apoapsis; getting into the elliptical orbit would have made for a cheap plane change.
(In this case the blue was a space station, and the cyan was its new solar array that ran out of fuel, so I sent a ship out from the station to grab the array and bring it back to the station).