2) It's clear from the context that it means the planet.Ok it's probably better to say "let's fly to the mother planet, Earth" because:
1. you fly to somewhere, not on somewhere
2. "mother Earth" sounds a little bit strange; without "planet", it is ambiguous (as if you have a mother and her name is Earth).
3. as far as I can tell, the construction is common in sci-fi, like "let's go back to the mother ship X" etc.
So I think "let's fly to the mother planet, Earth" is best ... what do you think?