"Solicitor is now saying that because monies have largely been distributed, my sister must return enough funds to cover the conveyancing fees. She is obviously unhappy with this."
Basically, your solicitor f**ked up.
The solicitor should have accounted for the costs of sale correctly before any money was distributed.
"... I was incorrectly charged the conveyancing fees,"
Yeah, that's totally wrong.
"...these should have been paid by the estate."
The solicitor should have taken account of the fees before distributing any money. It was totally wrong to apply all of the conveyancing fees to the share of the estate that was left to you.
"My sister thinks that I should bare the full costs of these fees as she has no benefit from this."
It is not your sister that will have to pay half of the costs but her daughter, your niece. The reason for this is that
"Sister decided to gift her half of the property to her daughter via a Deed of Variation"
A deed of variation changes the will so that the beneficiary becomes your niece rather than your sister.
"Who is right, legally? ethically?"
However, having said all of the above, the solicitor was the executor and they have a personal responsibility to get things right.
If anything, it seems as though you may have a claim against the solicitor to recover half of the fees from them personally because they made a mistake.
As another poster has said it looks like they may be trying to pass blame for their own mistake.
I would suggest that you go back to the solicitor and ask for the return of 50% of the conveyancing fees.