Ok Gregorvich made the wand, and Grindewald stole it from him. Dumbledore defeated Gindewald so the wand is now Dumbledore's. Now the Draco disarms Dumbledore so the wand is Draco's not Snape's because DRaco came in possesion of the wand before Snape could Dumbledore like planned. So when Voldemort takes the wand from Dumbledore's grave it is still Draco's because no one has defeated him. So when Harry steals Draco's wand which the other wand shows loyalty Harry becomes the owner the powerful wand as well as Draco's. So when Voldemort uses that wand against Harry while he has DRaco's wand the wand will not attack the owner of it. Any other questions or any clearing up as me.

What was the name of the wand?

What is this talk of side along apparation refering to?