I don't think it is Sphies core that is the problem but her balance, Brendan pulls her about from lift to lift and she is only on the floor for long enough to just get her balance when she is off again getting lifted.
Jo Wood suffered like this , Victoria Pendleton suffered like this and we know Victorias core had a so of steel.
The common denominator here is Brendan, that training last week showed how he is dancing for himself and viewing his partner as a prop to be moved about, look at Sophie's face in that, she hasn't a clue what she is supposed to be doing, Brendan hasn't articulated it to her.
I feel that Brandan has squandered Sophie's potential, she has to know what is expected from her, he can't just push, pull and place her about.
She needs to be told what is required and given a chance to get her own balance so that she can feel the floor and dance with balance.
Another dancer who does this to his partner is Anton, we see time after time him pushing pulling and manipulating his dancers around the floor, I don't think he can communicate to his partners what is required and so manipulates them about.
Oddly enough both of these are from first series, expectations of what celebs could achieve were probably different the and the 2 of them have not changed.
At the beginning of the series there was talk of Fiona having a lot of potential.
I feel both pro have squandered their celebs potential and I would love to see what they would be able to achieve with even 1 weeks teaching with one of the newer pros who have very different expectations of their celebs.