If the LA could prove that
"....the capital value of assets in trust (half share of house) are excluded from the assessment of means.....for means tested support from social services".
was a reason for setting up the trust it's likely they would do all in their power to include the half share. They would claim that there had been 'deliberate deprivation of assets' and add the value of the half share to your Mum's assets as notional capital.
It's strange that the solicitor put the suggestion of the trust in writing, normally he is so careful. I think perhaps because the Will created the trust then the LA cannot complain, the trust was designed to 'avoid' inheritance tax (quite legal) but as an inadvertent consequence of the trust it would also make the assets in the trust exempt from LA means-testing. The trust was not designed originally to deprive mum of assets.