First thing they should do is shuffle limbs around so there's one complete Alyssa and one compact limbless Alyssa, and hide the compact one.

Then they can tell parents that some anomaly happened and go to a doc to age the big Alyssa back up, and keep the small one as a pet in secret from their parents. Much to her protest at first, because they keep trimming her limbs so she can be hidden in their rooms, but she gets used to it quickly as she realises she can live an extremely lazy life and still be fed, cleaned and entertained.