So who is right ?

Obviously either Ann or Betty must be wrong.
Let’s recall the principle of relativity: All inertial frames of reference are equivalent
Do both stay in an inertial frame of reference?
- Ann (on Earth): yes
- Betty (in the Enterprise): no.
- While she is in an inertial frame during her travel to and during her travel from Alpha Centauri, she changes the frame of reference at least 3 times.

Obviously either Ann or Betty must be wrong.