Since we have gotten completely off subject...
Here is a fairly good article on the basics of Fusion drives.
How Stuff WorksAn Ion drive works in a similar manner but is not quite as sophisticated. (Ion drives are a reality, fusion drives are still theoretical and even more efficient.)
In any case, the drawback to both of these is that it takes some time to get up to speed. So if we're talking about travel from Cythera to it's moon(moons?), then it's impractical. Additionally, you can't use ion or fusion drive modules to escape the surface of a mars/earth/venus sized planet. It doesn't have enough umph...
An interstellar space ship wouldn't require any solid fuel rockets because that weight in fuel would be better spent on fuel for the ion drive. If you're going to argue to me that it would be needed to separate from the sky dock, I would say that the solid rockets could be attached to the sky dock and not the star ship.
Yes, solid fuel is cheaper and easier to deal with. But its not the most efficient for long term use.
Edit: I forgot to talk about this...
the op1 ship did had strap on chemical rockets, but the cinematic for op2 shows it using the fusion engine, it may have enough thrust to escape orbit, but in doing so it would have to use a lot of hydrogen to increase the mass of the exhaust so it could get the necessary thrust, that would deplete the storage very fast, and thus would necessitate the need to go to the gas giant
While this statement is true, it's not completely accurate. You're going to use the same amount of thrust to escape wether you use chemical or fusion/ion. If you say that a lot of the hydrogen would be used up to escape the gravity of Earth, then we have the same problem when we stop at a gas giant for fuel. Actual orbital mechanics wouldn't require you to break orbit in the first try. You can slowly work the orbit away from the planet until you finally break free. (Sort of the reverse of aerobraking.)