The commission which the party has set up under Lord Mackay was a good first step.
Appeal judges Lord Eassie, Lord Mackay of Drumadoon and Lord Wheatley have now overturned the ban.
Lord Mackay, sitting with Lord Phillip, ruled that the prison sentence should be reduced.
MSPs then quizzed Lord Mackay of Clashfern and Adrian Ward of the Law Society of Scotland.
Lady Dorrian, sitting with Lord Mackay of Drumadoon and Lord McEwan, issued a ruling on Wednesday, backing the midwives.
Lord Mackay said the appeal judges considered the case to involve careless driving falling not far short of dangerousness.
Lady Paton, who heard the appeal with Lord Mackay, said they would reduce McNeill's prison sentence to a 12-year term.
Conservative former Lord Chancellor Lord Mackay of Clashfern said further delay would be "inappropriate" after peers had carried out thorough scrutiny of the legislation.
Lord Mackay, who heard the appeal with Lord Philip, said they wished to consider their view on the case and would give a judgement later.
Mr Hague has been waiting for the report of an independent inquiry he set up last year under Lord Mackay of Clashfern, a former Tory Lord Chancellor.
Conservatives peer Lord Mackay of Clashfern said the "plain, clear, concise words" of the original Act that established the Health Service in 1946 should not be interfered with.
Speaking on behalf of the government, minister Lord De Mauley said Lord Mackay's amendment would require the state "to try to arbitrate" on whether a parent had taken reasonable steps.
The idea behind Lord Mackay's suggestion, he explained, was to impart that health service provision "is the final responsibility of the secretary of state... in ordinary language, 'The buck stops here'".
BBC: Cross-party talks to take place on health secretary role
Judge Lord Mackay heard Greens threw his victim down an embankment and beat her so badly that a passing motorist who came to her aid thought she had been knocked down by a car.
Towards the end of the day I'm in the BBC's somewhat Spartan studio at Lionacleit taking part in a discussion with the political presenter Colin Mackay, known to all and sundry as Lord Mackay.
BBC: NEWS | UK | Scotland | Rain, tiny planes and automobiles
Conservative and former lord chancellor Lord Mackay of Clashfern, who has commented on the legal status of the health secretary throughout the bill's time in the Lords, previously tabled an amendment to make the minister "ultimately responsible to Parliament".
BBC: Cross-party talks to take place on health secretary role
Mr Moynihan told Lord Mackay, sitting with Lady Dorrian and Lord McEwan, that in so far as the women were part of a team their right to conscientious objection extended to the whole of their duties, save for the provision that there was an obligation to participate in life-saving measures.
The case was heard at the Court of Criminal Appeal in Edinburgh by Lord Clarke, sitting with Lords Mackay of Drumadoon and Drummond Young.
Bluebirds fan Lord Kinnock hosted the party, which was attended by owner Vincent Tan, manager Malky Mackay and captain Mark Hudson.
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