So you don't believe she loved either of them ?
I'm going to say she was probably unable to give unconditional love to either of them, stemming from that she'd never experienced it. Love, in the form that children need to be shown in order to feel, seems to have been taboo in some deeply religious households. Children were taught about a God who didn't love children who were naughty or disobeyed their parents. Somehow, the parents would feel that if this was ok for God, it was the way they should conduct themselves, thus children were never praised for getting it right, RIGHT was what was expected of them, but were reprimanded for getting it wrong. Naturally, this didn't stop "things" being heaped on them because it wouldn't have done for the outside world to see that, as a parent, they were a failure, which was how they would see themselves if their children wouldn't conform to the standards set for them. I think June was deeply disappointed in both Sheila and Jeremy. I don't believe either were what she'd had in mind that her children would be. I get the impression that she thought she might stand a better chance with the twins.