Discuss the development and changing issues and images of women in Gothic vampire literature (in general, historically and in regard to Stoker's Dracula, Carter's "The Lady of the House of Love," and Meyer's Twilight, with quotations and examples from each book).

Women in vampire literature tend to be seductive vampires themselves or victims of vampires. Interestingly, in the stories mentioned in your question, much is suggested about the social entrapment of women, whether these women be ordinary humans or vampires. Early vampire novels featured both male and female vampires, the most famous of the latter being the titular character of Carmilla.
Dracula says much about society's ambiguity regarding the changing gender norms for women in the late Victorian period. There was a rise of women in the work force, and men feared that women were intruding upon traditionally masculine spaces. Stoker presents these sentiments in the characters of Mina and Lucy: both women mix and match qualities associated with the Victorian ideal of womanhood and the New Woman. Lucy is open about her sexual desires, but she still stays home and chooses to marry. Mina works and knows how to use a newfangled technology like a typewriter, yet she is also devoted to the men in her life.
When transformed into vampires, the women in Dracula become more aggressive and openly sensual. They prey upon human men, evoking the fear of feminine domination over a male-dominated world. During his imprisonment in Dracula's castle, Jonathan is particularly unnerved by the power of the brides, even comparing them to a normal woman like the virtuous Mina, saying, "I am alone in the castle with those horrible women. Faugh! Mina is a woman, and there is nought in common. They are devils of the Pit!" In this way, Mina is portrayed as a kind of ideal woman, while the vampire women are decidedly unnatural.
In spite of the power of the brides, vampirism is not liberating in any sense for the female characters. As Dracula points out, once under his control, the women become his, and he can do whatever he pleases with them. No matter what, women in Dracula cannot escape such control, human or vampire. However, it must be said that Mina is an intelligent, active character, a decided contrast to the traditional Gothic heroine who is usually passive in her tribulations against predatory masculine forces.
Carter's "The Lady of the House of Love" is quite subversive in its take on the female vampire. Countess Nosferatu is a predator toward young men, which is a reversal of the usual male vampire on the lookout for young women. Unlike the brides or Lucy in Dracula, the countess seems to exist outside of male control, as she lives as the mistress of her own crumbling castle. However, Carter subverts even this image of the powerful femme fatale by making her monster vulnerable.
When Countess Nosferatu's final victim comes calling, he does not see her as a femme fatale, but as a lonely soul. The language used to describe her does not suggest power, but actually a lack of autonomy, as though her vampirism controlled her:

Her voice, issuing from those red lips like the obese roses in her garden, lips that do not move—her voice is curiously disembodied; she is like a doll, he thought, a ventriloquist’s doll, or, more, like a great, ingenious piece of clockwork. For she seemed inadequately powered by some slow energy of which she was not in control; as if she had been wound up years ago, when she was born, and now the mechanism was inexorably running down and would leave her lifeless. This idea that she might be an automaton, made of white velvet and black fur, that could not move of its own accord, never quite deserted him; indeed, it deeply moved his heart. The carnival air of her white dress emphasized her unreality, like a sad Columbine who lost her way in the wood a long time ago and never reached the fair.

By comparing her to dolls and clockwork, the Officer is painting the female vampire as a damsel of sorts, someone who needs to be saved. This is a decided reversal from the reader's initial impression of the countess. Carter further suggests Countess Nosferatu is a prisoner of her own lifestyle, and perhaps also society's restrictions, by using the caged bird in her room as a symbol of her own state. In the end, when the countess does become human in a sense, she dies, unable to escape her prison.
Compared to Dracula and "The Lady of the House of Love," Twilight does not seem to contain as many ambiguities about women in Gothic vampire fiction. Bella is closer to the traditional Gothic heroine for much of the series, as she is rather passive initially. However, once she transforms into a vampire later in the series, she changes, becoming more powerful both physically and mentally. Unlike Mina, who sees transformation as damnation, Bella sees it as something positive which allows her to be closer to her beloved Edward, who is less a predator of the night and more of a misunderstood Byronic hero. She also becomes more confident and graceful, a total reversal from the shy, clumsy girl she was at the beginning of the series.
Some critics have noted Bella's transformation makes her even less relatable than she was before and that it is a negative development, since she gains all these abilities and traits only when she gives up her original identity to be with a man. However, in the book itself, this transformation is viewed as positive and a natural happy conclusion to the series. Bella herself sees it as such in Breaking Dawn, scorning the human she was:

I'd never been strong enough to deal with the things outside my control, to attack the enemies or outrun them. To avoid the pain. Always human and weak, the only thing I'd ever been able to do was keep going. Endure. Survive.

Only in vampirism can she live a fuller life and go beyond mere survival, or so she believes.
Comparing all three of these stories, one can see a trend of discussing the restrictions placed upon women by society and exploring potential avenues for liberation. In Dracula, women are entrapped no matter what they do, whether they be New Women or vampires. In Carter's story, even a powerful vampire is a prisoner of her own desires and social role, unable to escape in the end. In Twilight, the vampire transformation is viewed as something positive and even as a coming of age for the heroine, but this happens arguably at the cost of her own identity. It seems that no matter the age, the role of women in Gothic vampire fiction is one of ambiguity, seemingly powerful and entrapped all at once.