Mostly directionally from the Sun. Reflected radiation comes from the reflection surface. Cosmic background from dark sky (which isn’t all directions if you’re near a blocking body).
That said, the point of these studies is to measure how much damage which kinds of radiation cause. So short answer, we’re not sure. (But probably the Sun.)
Now I'm wondering, if you go from the space ship, say 1000 km into the direction of the Sun, and then somehow apply a very small force to the radiation, would it be possible to make the radiation go past the space ship?
For charged particles, yes. This is how the earth’s magnetic field [1] protects us.
[1] https://en.m.wikipedia.org/wiki/Earth%27s_magnetic_field#Mag...
1. Trapped protons and neutrons in the Van Allen radiation belts. The ISS is well below the first Van Allen belt but it is really a continuous spectrum with peaks and valleys. For example there is the South Atlantic Anomaly where the inner radiation belt dips lower and flying through this region exposes you to more radiation. This is the fairly distributed radiation source
2. The sun. Solar storms, coronal mass ejections, all of these increase radiation. Although these may not be facing the sun as much as you might think. The radiation bends around the magnetic field of the earth so this often affects things closer to the poles of the Earth (and causes the Auroras) and spacecraft in high inclination orbits.
3. Galactic Cosmic Rays (GCRs). These are from far off events like supernovae or black holes but are really high energy. So direction is generally "from the galactic disk" but that is a pretty wide direction
4. Bremsstrahlung. This is basically radiation caused when one charged particle deflecting/slowing down another particle. The interaction causes some radiation (usually in the form of X-rays, or gamma rays if you get something coming in real hot) but basically comes out as the vector component of how the particle was deflected so it can be from a number of directions. https://en.wikipedia.org/wiki/Bremsstrahlung#In_astrophysics