What happens when a ship pushes a figure sideways into another ship? Does this prevent the ships from closing rail to rail? What about a figure caught between a sandbar and ship, or rock and ship? Can this prevent the ship from being dashed upon the rocks or does the figure just get pushed out the nearest end?

There doesn't seem to be anything about it other than a section under Sailing the Ship:

Colliding with Figures: Figures that a ship collides with are simply pushed ahead of the ship (even if soaring, since otherwise situations could be created where multiple figures are in the same space). No damage occurs to either the figure or the ship. If a figure is pushed off the edge of the map, that figure is considered to have fled the encounter.

That is the complete, and exact way it's printed in my copy (North American Ed)

Veritech said:

There is nothing to stop the figure that is being pushed from being pushed on to the other ship. So that is what happens.
The figure is pushed and there is only an issue when the figure is being pushed into a space it cannot enter.

At least, that is the way the rules work, until we hear otherwise.

Veritech said:

A figure can be pushed onto a sandbar, as sandbars do not prevent movement. A flying figure could be pushed onto a rock. We included a question about what happens when a figure is pushed into a rock by vessel movement in the recent document sent for FAQ assistance, so hopefully there will be an answer to this in the next FAQ. In the mean time there is no guidance at all, except perhaps the example of a crushing wall, which says the figure would die. But it is also possible that FFG will choose other options.