Go back before you started the dlc. Wprse case scenario is you have visited the castle before and depending on how far back ago that was you may have to forgo the dlc. The same thing happened to me but i started a new character as i literally beelined straight to the dlc at the start of the game.

Did you visit the castle before finding Serana? That's a known bug if she won't open the gate because she improperly initiated the gate opening dialogue when you first free her from Dimhollow Crypt. I believe you can wall clip through the gate from the right railing to reach the door itself and enter but I've never done it.