I just realised that Mira HQ won't be taken over by the impostors because in the alternative world they stop the ship that carried the parasites that started the entire thing.
Which means that Purple's family aren't impostors and they'll probably have to see Purple as an impostor.
Aswell as when Purple turned into an Imposter we could see small shots of what seems to be the future so maybe Purple had a reason that they didn't want to go to Mira?