Gay and lesbian rights in hospital settings have been disputed for decades. Today, some states have laws in place to protect partners and others states do not. When it comes to delivering a baby, women are allowed to have coaches or family members of their choice in the labor and delivery room, in most hospitals, so having your partner in the room shouldn't be an issue. If you simply want your partner in the delivery room you can address her as your birth coach and no one will ask another question.
However, legal rights to the infant after birth is a different story. Lesbian couples are best served by finding a hospital that meets their needs before labor begins. In some cases legal documentation can be setup so your partner has legal rights to parenthood before birth, but again laws differ by state. In extreme cases, couples move to states that recognize same sex partnerships before giving birth to ease the process.
