I have the same question, but about a more realistic problem. Andromeda is coming. How do we:
1. Maintain presence in the Milky Way if all our star systems get ejected?
2. Colonize Andromeda by sending a one-way mission to it?
The Delta-V for galaxies surely must be insane. How do we do that?
ETA: Two days acceleration at 1 m/sē ought to be enough to put you in either galaxy, it's barely 20 times ISS orbital speed, I don't think Epsilon Eridani would be much more of a problem. I would assume firing a large five-stage array of good old chemical engines for a few hours to a day or two would solve both problems.