Jack McConnell has come under mounting pressure from churches, political opponents and rights campaigners over his refusal to make his position clear, which he justifies on the grounds that immigration policy is a reserved matter for Westminster.
The SNP hoped to put the First Minister on the spot yesterday (Thursday) when it used its parliamentary time to debate the issues.
Meanwhile Sheena Wardhaugh, the EIS vice-president, who is from the union's South Lanarkshire local association, queried Mr McConnell's defence when she pointed out there are various legal statutes affecting children of asylum-seekers, all of which are the responsibility of the Scottish Parliament.
Among them are the Children (Scotland) Act 1995 and the Standards in Scotland's Schools Act 2000. These apply to the children of asylum-seekers as much as they do to other children in Scotland, Ms Wardhaugh said.
Ms Wardhaugh, addressing a rally attended by an estimated 1,000 people calling for Dungavel's closure, expressed concern at the limited facilities at the centre where education is voluntary and limited to 20 hours a week.
Fifteen children were admitted in July this year.
The SNP upped the ante this week by accusing Westminster of espousing "right-wing racist policies" in its approach to immigration. The party said that Scottish Executive ministers had been misled by their London colleagues. Weekend reports claimed that Jackie Baillie, the then Social Justice Minister, had won an assurance in 2001 from Lord Rooker, a Home Office minister, that children would only be detained as a last resort and for a matter of days. Some have been there for more than a year.
Ironically, when it housed convicted prisoners preparing for release Dungavel was an open establishment. Now it is surrounded by high barbed wire.