Travelling famillies - a lesson for all would-be relativists

There now follows a demonstration of what Special Relativity (SR) can get up to given it's wicked way. In particular, the misunderstanding of the term "Inertial Frame".

Suppose we had a brother and sister on earth, in fact identical twins. We will call the brother "Mahal", and the sister "Chere".

Chere, the rocket scientist, invents a powerful rocket capable of near light speeds, and plans a trip to Proxima Centuri , the nearest star. Mahal, however, does not like flying, so decides to stay at home.

On their 25th Birthdays, Chere blasts off attaining a speed of 86.6% the speed of light. As the distance to promima Centuri is 4.2 light years, it takes her 4.86 years to get there. She stops, turns around, and blasts back, taking another 4.86 years to get to earth, making the trip time about 9.72 years. The equation used can be seen in the following LINK (equation 1)

The point is, because Chere has been travalling much faster them Mahal, her time has slowed down a bit, and when she gets back, here own "twin" is much older than she is! There is a better example of this HERE

All things being equal. this has been exprimentally proved, and that this is what happens. However, if relativity is right, we could just as well say that from Chere's point of view, it is Mahal who rushes away from her at 0.866c, so it would be him who is the younger when the trip ends? So who is right? They can't both be!

It is exactly this type of question that stumps those who tell us "Oh, I know all about Relativity".

Is anyone able to tell how to figure it out ( you would need a thorough understanding of the subject to be correct!)? I have left a clue - the second sentence.

This is a subject very dear to me, hence the character names. "Mahal" is "dear" in Tagalog (chosen because the twin who stays is (M)ale), "Chere" is "dear" in French (chosen because "Chere" is the French feminine adjective).