Rowena's situation

Yes, Eugenia was older.
As for Rowena, the film does not say that she could not have children, just that she had not yet conceived. Back then, a woman who was not pregnant within a reasonable time after her marriage provoked the suspicion that something was wrong either with her or with the marriage. In addition, Rowena's mother and sister both seemed able to breed like bunnies. Rowena's anxiety might have been a natural result not only of a thwarted desire to get pregnant, but also of her perception that she had failed the expectations of both her family and her society. Even today, many women who are childless by chance (not choice) often view themselves (and are viewed by society) as defective, and not real women.

It was common for the eldest sister to wed first. It was considered a failure as well as humilating for the elder sister(who presumably had been out[in society] longer) to languish on The [marriage] Market while her younger sister was whisked to the altar.

The book also does not explain Rowena's inability to get pregnant. Rowena suffers greatly on account of it, to the point of begging to hold Eugenia's babies when Eugenia wants them immediately put to bed.

If you read the book there is a lot of comparison between the Alabaster household and an ant colony. In an ant colony there is only one queen, only one female ant that lays eggs and reporduces. Lady Alabaster was the "queen" ant, therefore the one that was able to breed. When Eugenia married, she took over that position and therefore she was the one that was able to breed, not Rowena. It also explains the incest thing.

I would like to go further with this question and also ask if we are to believe that all the children of Eugenia's are hers and Eugenes? We come away with that knowledge but does that mean that William was impotent? I mean she couldn't be "careful" or he would have really known the children weren't his(as he did indeed intimate).