Suppose I have a very powerful and durable rocket that is able to reach speed of light minus $10^{-1000^{1000^{1000}}}$ in $10^{-1000^{1000^{1000}}}$ milliseconds. Very instant acceleration. I can also adjust the amount of acceleration. I want my rocket to travel to a location that is 1 light-year far from earth, and turn back. I want my rocket to come back as soon as possible according to my watch.
Is it approximately 2 years?
How much time would pass according to my rocket's watch?
Would the result be different if I want my rocket to come back as soon as possible according to its watch?