The thing with Custis is that before the war, he inherited Arlington when his grandfather died. When the Civil War broke out, the Union confiscated Arlington and created the cemetery in Mary Lee's rose garden. Years after the war, he was able to get his property back by a court ruling, but with thousands of graves that would have needed to be moved, he instead sold the property to the government. Until then, he didn't have much to bring into a possible marriage, least of all a house to live in. The house in Lexington was the property of Washington & Lee and the Lee family lived in there only as long as first General Lee and then Custis was president of the college.
As to Lee's daughters, Agnes came close to marrying. But he was killed during the war. And she died not long after the war ended. Anne died during the war, in 1862. After her mother's death, Mildred was more or less the lady of the house, living with Custis when she wasn't traveling. And Mary was traveling all over the world. I read somewhere that she had an independent character. For her, marriage might have felt like being trapped.
I would also think that with Lee being so revered, courting one of his daughters and asking the general for her hand in marriage might have been a daunting task to many a possible suitor.