Vader did use the Force while piloting a starfighter (his Eta-2 interceptor) at least once:
[Isval] looked up through the canopy of the escort boat, eyes wide with disbelief, to see the shuttle, merely tens of meters distant and flying upside down. The ships’ cockpit viewports faced each other. Isval could see Vader, and Vader could see them. Vader made a gesture with his gloved hand, as if he were pinching off a bleeding artery, and Isval felt her throat constrict. Instinctively she reached for her neck, but there was nothing there, just the pressure, just the squeezing. She couldn’t breathe! She pawed at her neck, panicked now, legs kicking. Beside her, Eshgo was behaving the same way. She fought to draw breath, couldn’t. She clawed at her collar, squirmed in her seat, made a tiny gasp. Whatever held her squeezed tighter, tighter.
“What’s wrong?” Drim shouted from the back. “What is it? What is it?”
Her vision was darkening. Little bursts of light swam before her eyes. She remembered the sounds Pok had made over the comm when Vader had killed him—the long silence punctuated by the abortive gasps.
It was Vader choking her somehow. It had to be.
She glanced up and saw the Imperial shuttle, with Vader at the controls.
Someone was calling her name. Cham? Drim? Faylin?
She couldn’t answer. Her mouth wouldn’t work. She had no breath, no words. Her vision tunneled down to Vader, only Vader. She imagined herself reflected in the eyepieces of his helmet. Her world distilled down to his eyes and her anger, and that distillation gave her a moment of clarity.
She was failing, she knew, dying, but she wouldn’t go alone.
Lords of the Sith, p. 141
In that case, however, it was an unusual situation in which Vader's ship had a matched velocity with the enemy ship and Vader could see the people in the enemy ship. This suggests that it's generally quite difficult to use Force powers against such fast-moving targets as other spaceships. It's much easier to use the starfighter's other weapons, which are so relatively easy to use that even a pilot who is not Force-sensitive can use them. This is similar to why Jedi who have mastered tutanimis (dissipating concentrated energy, like that of a lightsaber blade) would still use a lightsaber to deflect another lightsaber blade even though they could theoretically block a lightsaber blade with their bare hands -- it's simply a lot easier and requires less concentration to use a purpose-built weapon than use the Force to accomplish the same goal.
Regarding your specific examples:
In Revenge of the Sith, Anakin's and Obi-Wan's fighters are overrun by some droids that start to disassemble their fighters. Neither uses the Force to move them away.
You are right that the Jedi probably could have used the Force just as easily here since the droids were stationary relative to the Jedi pilot. This is probably best explained as they simply didn't think of it in the mayhem of the battle (there were many other threats vying for their attention in addition to the droids). Since they were already focused on flying their fighters and using their blasters they probably just didn't think of using the Force at that time (when you have a hammer, every problem looks like a nail...)
In Rogue One, Vader uses a combination of lightsaber and Force techniques to make short work of the Alderaanian soldiers, then the corvette Tantive IV launches, a few meters away from the dock. Why didn't he telekinetically disrupt one of its engines to stop it?
The Tantive IV is a pretty big ship relative to a human like Vader so it's probably fairly difficult to stop such a ship with the Force in only a few seconds before it jumps to hyperspace. Additionally, Vader likely figured he could easily track it and capture it after a hyperspace jump (which is exactly what happened).
Then we see Vader participating in a space combat (interestingly, for the only time in the old movies) in the Death Star trench. He is seen locking on Rebel fighters in front of him and shooting at them, while it would be easier to disrupt their course and make them crash on the trench's walls.
It's arguably easier to use his fighter's blasters (which are designed to destroy enemy fighters) rather than try to push a relatively big ship enough to make it crash.
It's worth noting that in the Legends video game Star Wars: Jedi Starfighter a Jedi pilot uses the Force against enemy fighters (including Force Lightning!).
