Long before the sun expands, we will have encased our solar system in a metal eggshell, installed a new man-made sun and then deactivate the old one.
Or we'll strap engines on the Earth and move it to a younger vibrant sun somewhere else.
That would simply not work. We may figure out how to learn how to move through space-time in a fashion simular to how a warp engine in Star Trek does it. But a gravity well as large as Earth would not be moved cheaply or easily. Not to mention how badly damaged and frozen it would b for eons before it could reach another system.
They slowing it down, and fitting it into the right zone in the new star's orbit in a balance with other planets is equally as problematic.
It is far better to move life to another ball of rock in another solar system. Even if you had to do it on a ship so slow it takes generations of humans to do so.