Legal legitimacy
In Wharton's era, there was a legal and economic distinction between children born in or out of wedlock. For the most part, men controlled the money, wealth, and property. When a woman married, her husband generally assumed control of whatever assets she owned. All of this property was passed on to their children. With no reliable form of paternity testing available, people generally assumed that any children born to a married woman were fathered by her husband. As such, they had the legal right to inherit his property when he died. In the upper classes (such as the one that produced Wharton herself) that could mean the difference between being independently wealthy from birth and having nothing. In an era with little public education and no social safety net, "legitimacy" or being born to a married woman could mean the difference between life and death.
This novel was written before the invention of child support. Tina had no legal claim on any financial support from her father or on any part of his estate if he died. But when Delia adopts her, Tina takes on the social class and status of her parents.
Motherhood
Charlotte is the person who gave Tina life, and who attempted to provide for her by placing her in a foundling home. They had occasional contact, but Tina did not know anything about her family of origin. When Delia adopts Tina, she becomes Tina's legal mother and takes responsibility for Tina's education and introduction into society. This is a time consuming and expensive process. Tina has an emotional bond with both women, but the novel raises the question of what it really means to be a mother. Both women feel as though they are worthy of the title, and both love Tina and feel a sense of responsibility toward her.
Propriety
Charlotte concealed a pregnancy and abandoned her daughter to a foundling home because if the circumstances of Tina's birth became known she would no longer have a good, respectable social position. In Wharton's era, it was not socially acceptable for a woman to be divorced, let alone for her to conceive and bear a child while unwed. No man of her own social class would be willing to marry her unless he publicly acknowledged the child as his own, in which case the time to marry would have been during the pregnancy. Charlotte could not afford for her soon-to-be-husband to find out about Tina. Delia, however, was already married and could adopt Tina (another option not available to Charlotte).
There is a gigantic double standard in the book in which the activities thought right and appropriate for men are unacceptable for women. It was improper for Charlotte to become pregnant and have a baby, but it was socially acceptable for her baby's father to abandon her once she became pregnant. Nothing bad happened to him as a consequence of his behavior.
Marriage, for most women of Wharton's era, was evidence of propriety. Having a baby, like many other privileges restricted to married women, was only one of a multitude of things unmarried women were not allowed to do without serious negative consequences.
Family Tendencies
One of the things that compels Charlotte to share her secret with Delia is the fear that Tina's behavior will mirror Charlotte's: Charlotte is afraid that Tina, like Charlotte herself, will succumb to a love affair and get pregnant.
