Justin is right on the money here. You have zero bargaining power once you've reenlisted STAR. However, just as Justin pointed out, if you wait and desire to rotate to shore earlier than the normal sea shore rotation date, being able to pull out the reenlistement card puts the power on your side.
Justin's situation is all too common even with today's manning issues. The STAR reelistment is only good for certain people in certain circumstances. Make sure the guys thoroughly research this option.
Now, if one of the guys does well, and the manning supports, the Staff Pickup (aka JSI) is a good option for some. This requires the STAR reenlistment option, but the two years you add to your contract is spent at NPTU. Many pros and many cons to the SPU/JSI route.
Either way, best of luck to the twins!