Oscillation in tilt of the solar system
The tidal field of the Galaxy does lead to the oscillation of the plane of very wide binaries.  The mechanism of this oscillation is identical to the Kozai-Lidov mechanism (the only difference is that in the case of KL oscillations the tidal field is generated by the averaged orbit of a tertiary stellar companion).

However, if you run the numbers, the timescale for these oscillations is extremely long for any of the planets (I forget how long exactly, but much longer than the age of the Universe).  It's somewhat shorter for comets in the Oort Cloud, only a few billion years, because their orbits are much larger and so would tend to experience larger a larger tidal effect.