After I get the Moth priest Blade and read the Scrolls I tried to leave but the exit has a gate and the Dawnguard are on the other side with Serana. I've defeated the Dawnguard with shouts but the gate never lowers and I'm trapped in the Ancestors Glade. Why is this happening?
This glitch occurs due to you not having Serana follow you during this quest. From this thread:
When you have to go to the Ancestor Glade to read the Elder Scroll on the Dawnguard side, if you DON'T have Serana following you and have her wait somewhere, a glitch follows. When you enter the glade, Serana will automaticly appear at the start of the cave, but won't move. When you talk to her, she's already "following" you, but she isn't because she's standng completely still. I continue, thinking she'll catch up. I go on and read the scroll... Objective updates to tell me to "Speak to Serana", problem is, the door leading out is barred up, with no way out. Completly sealing you inside the cave. So unless you have a back-up save before this happens, you're stuck there for all time.
tl;dr: You're going to need to reload your last save.