You might want to try looking through the birth marriage death index using her maiden name. Someone once told me, not sure never did anything on Eva, that her parents married when Esther was pregnant with Eva.
Esther was 43-ish when she gave birth to Eva and had already had several miscarriages by the time Eva came around. I assume she was with Ben Hart when these miscarriages occured. I don't know, but I would have thought that had they been together during that time they would have married before Esther became pregnant with Eva. Just a guess.
According to Eva's autobiography, "Titanic Survivor", Esther Hart had been in an abusive marriage for many years and had something like twelve children, all of whom had died because of her husband's treatment. I think the implication was that they were born unhealthy because of Esther's physical condition stemming from her abuse, rather than that their father harmed them directly.
As Eva tells it, after being liberated by her husband's death, Esther gave up all thoughts of marrying again, until Benjamin Hart pursued her and finally won her over.
I have no idea of whether or not it was a shotgun marriage. I'm sure it's easily enough to verify either way.
Eva's mother felt a presentiment as if something was to happen to the ship. What struck me was that his intuition was so great that Eva's mother slept during the day and stayed up all night until dressed. Almost all interviews Eva talks about the premonition of his mother.