You're completely ignoring the time dilation effects of relativity. From the perspective of a fast moving spaceship, the distance between stars contracts, and from the perspective of an outside observer, the time experienced in the spaceship slows down. This is why I believe that interstellar travel will be feasible, although creating any sort of empire will be impossible. Here's a quote from the Wikipedia article on time dilation:
"Theoretically, time dilation would make it possible for passengers in a fast-moving vehicle to advance further into the future in a short period of their own time. For sufficiently high speeds, the effect is dramatic.[2] For example, one year of travel might correspond to ten years on Earth. Indeed, a constant 1 g acceleration would permit humans to travel through the entire known Universe in one human lifetime.[12] Space travelers could then return to Earth billions of years in the future. A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle, and the Orion Project has been an attempt toward this idea."
3. A spacecraft made of material so strong that it can survive collisions with rocky material at velocities very close to c. Or a Star Trek style deflector shield.
Warp drive is probably easier to achieve.
Detonating nukes behind your spaceship will never give you anything close to 1G constant acceleration over a long period of time.
Time dilation has some definite drawbacks as well. Say for example you have a very redundant ship that can repair damage from micrometeorite attacks in a few minutes. The hits are very rare, maybe once a year at most at normal velocity. But now you're traveling at a high fraction of C and you're hitting tens of fragments per second, and always at a high fraction of C. Your repair process is effectively working in slow motion and could very easily get overwhelmed. Without a sci-fi energy shield your spacecraft is ablated to death long before you get anywhere.
"Theoretically, time dilation would make it possible for passengers in a fast-moving vehicle to advance further into the future in a short period of their own time. For sufficiently high speeds, the effect is dramatic.[2] For example, one year of travel might correspond to ten years on Earth. Indeed, a constant 1 g acceleration would permit humans to travel through the entire known Universe in one human lifetime.[12] Space travelers could then return to Earth billions of years in the future. A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle, and the Orion Project has been an attempt toward this idea."
https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_di...