The atmosphere gets denser as you move towards ground level. If a meteor hits the atmosphere at an angle it can reach a certain depth before it skims off, a little like skimming a stone on the surface of a lake.
It is fully possible for an incoming meteor to hit the atmosphere at an angle, to begin burning up, to lose mass, and to reach a point in the atmosphere where the density is sufficiently high for it to skim back up into space. This, to me, sounds exactly like what you've observed - a meteor (or shooting star) burning up (leaving a trail) and suddenly changing direction (as it skims off some dense-enough region of the atmosphere).
This is also a problem for vehicles, like the shuttle, re-entering our atmosphere. There is a very narrow angular window they have to hit. Too steep an angle and the density of air increases too rapidly, causing excess heating and ultimately failure of the heat shield. Too shallow an angle and the craft skims off the atmosphere back into space. The Apollo 13 astronauts, with their navigation systems shut down, needed get the angle right by 'eye' in conjunction with measurements from the ground!