Basically, I found an everstone on my HG but my shiny mudkip which was transfered to me is on my pokemon black. Can i get a pokemon to hold the everstone, transfer it over then give it to my mudkip?
No, you cannot transfer Pokemon with Items. The Game will ask you if the items can be removed so your Pokemon can be transferred anyway. Game Freak did this concept because they want to avoid things to be transsferred that cant be found in Pokemon Black or White, for example TM Dark Pulse.