Unfortunately doing both isn’t possible. What you can do, however, is play through the Dawnguard Questline to completion. At some point after you finish the final quest, Serana will offer to give you her blood - giving you access to being a vampire lord. You won’t be able to do the Dawnguard missions as a Vampire Lord, because if you take the gift from Harkon himself, you immediatly become an enemy to the Dawnguard faction.
There are mods available for exactly what you are wanting, I am sure.