What would happen to time perception is we were exactly still?

Sorry if I'm asking in the wrong place.

I was having a conversation with my son (13) last night about time being perceived as slowing as the speed you travelled increased. He then asked if we were totally still (as in not on the Earth travelling around the sun travelling around the Milky Way travelling through the universe) what would happen in regards to our perception of time.

If we were able to travel at such a speed (hypothetically, obviously, so no arguments that we can't please, even though I appreciate that it's true) that allowed us to perceive that we've travelled for 1 year in a round trip, but when we returned 2 million years had passed, if we were totally still would time begin and end for us simultaneously or would it become infinite and would we experience a sort of immortality?

Any answers would be greatly appreciated.