They could be cousins twice removed. But "The Cousins' Paradox" doesn't quite have the same ring.Hello again.
One last thought.
If the travelling twin passes the stay at home twin on his outward journey and is the same age he cannot have been born at the same time. If they were born at the same their travel histeory i.e spacetime intervals covered, are differenttime they cannot be the same age. Time dilation between moving frames or something along those lines.
Either way they are not twins in the normal sense of twins.
Twins are used as a sort of shorthand (perhaps not intentionally) meaning "two of the same". So the twins could just be two copies of the same person, the traveller takes out some sort of special insurance, by jumping in the Duplomatic 2000 and making a back-up copy of herself. Then she gets fired off into space reaching cruising speed after a very short period of time and sails off to some destination, then turns around, reaches the same cruising speed in the opposite direction (again very quickly) and returns to see how the copy is going. The copy is older, and pissed. They get in a row and the older, stay-at-home copy loses it and goes on a rampage, leading to a confusing car chase with people shooting at each other for no readily apparent reason. In the end, you find out that in fact both were copies and the real original had gone off in another space ship which went much faster than the first and hence the original is still young and beautiful when she gets back and marries the policeman who solves the case by accurately shooting the bad copy (twice, because you thought she was dead, but she wasn't really the first time). Just before the credits begin to roll, you learn that the policeman is actually a grandson of the copy he just "retired" (he was raised by an Angolan sheep herder, so he never knew).
Oh, hang on, that has nothing at all to do with the original twins' scenario.
Feel free to pick holes in my alternative scenario.
(Sorry about that granpa, it was just that the small-mindedness got to me for a moment there )