The orbits in our solar system add up to a certain total angular momentum, which is a vector so points in some direction. To get that vector to point some other way requires torque, it won't happen just because the solar system is orbiting the galaxy. So the "precession" rate of the plane of our solar system is controlled by very different things than the orbital rate, so there would never be any reason for picture #1.
Picture #2 is what you get if there is no torque, so at least there's a reason for it. The kind of torque you'd need would be a force that points up from the plane on one side of the orbit and down from the plane on the other side, but a force like that would depend on distance from the Sun so it would be different for different planets. That would tend to make their orbital planes undergo nodal precession at different rates, so they would not be in the same plane. So either such torques have had no effect over the lifetime of the solar system, or else something else shepherds the planets into the same plane. But it can't be the latter, because Neptune is in the plane but Pluto isn't. So I think it must be picture #2.