Dracula and Carmilla have never seen eye to eye, especially in Vampire Hunter D: Bloodlust.
In fairness, Bloodlust is loosely based on Demon Deathchase, and doesn't represent their in-novel relationship as well. I don't think, anyway.
But even so, I do like the sentiment in your post. I think that would be an interesting parallel. We've seen in CotM that Carmilla is willing to work with Dracula, but I think it'd be a cool take if Carmilla either worked with Dracula waiting for the opportune moment to usurp his power, or to work with the protagonists against him and become the antagonist once he's beaten.
since I think Dracula isn't the first vampire and I think there should be vampires that are much older than him
I like that idea. Depending on whether you go by the Castlevania or Stoker mythos, Dracula can either be the Dark Lord or just a greater vampire. Stoker's take on him, I think, paints him as a powerful vampire with considerable wit and influence, but isn't exactly THE vampire or by any means the oldest or strongest. It's never really detailed in Castlevania whether or not he's the original, only that he's the strongest due to his black magic and age (since vampires almost universally get stronger as time goes on).
I think your take is a very unique one. All too often Dracula as a character is portrayed as THE bigbad, or one of the biggest fish period. The idea of lesser vampires plotting a coup de'tat to preserve their own status quo is one I can definitely get behind.
As for the Castlevania's lore on turning a human, I don't remember if it's ever actually specified. There are some lores that go by a certain number of bites, some by where the human's bitten, etc. I'm partial to the Hellsing/Anne Rice mythos in which the human must have all of their blood drained, and then drink the blood of a vampire to turn, and have a cycle of full-blood transfusions before the turning is complete. In this way, the human's blood is cycled through the vampire multiple times until it becomes vampiric, and then the human is "refilled" with vampiric blood. Whether or not the human chose to be turned or willingly offered their blood to the vampire(s) in question can also play a part.
I think a certain catboy said it best:
"Blood is the currency of the soul, the vehicle of life. Having blood offered...is a very different experience than taking it."