well if you arent simulating the entire galaxy rotation and galaxies moving away from each other and stuff, then you could cut corners on more things, because calculating everything sounds like a lot of math.
planet 1 is a position X, planet 2 at B now, depending on the situation you would want to WAIT for your launch because another date will provide an EARLIER arrival, for example, if you go all simulator-ish. Also imagine the planets orbits moving them in a way that the sun (or another planet) is on the way, your ship will go through it.
I assume you have orbits a a mathematical function?, for in-system travel I'd suggest you calculate the distance to travel at launch, set that as a the travel distance no matter what (even if the planets are accelerating away from each other at the time), and update the travel % each tick if you must (you don't need to know the planets current position for this btw, and no you dont need to update the % every tick either).
Then when you need to display the ship on screen, just make a nice spline curve that follows the possible orbit (or counter orbit) between the current position of both planets and set the ship at the correct % of the way, regardless of the actual current distance seen vs traveled, doubt anyone will notice you are off a few light years, or care, even if they do notice. Doing this you could solve the "planet in between" issue by detecting if your ship is inside a planet, and adding an "slingshot" curve around that planet, then draw the ship using it as a slingshot.