Incidentally I have lost a lot of respect for Sweden.
There are some lines that should not ever be crossed - and State interference with a functioning family not short of love is fully worthy of condemnation... T_T
I am angry because not everybody's story ends well. I wonder if your family qualifies for political asylum or some such status (kind of depends on whether there is a non government organization who profits off of such).
That could be possible, the Romeike family from German was granted asylum in the USA on the grounds of not being allowed to homeschool in their home country. This was not an easy process for them and I do not think that would be a good idea for @markwhittam and family. It is still legal to homeschool in most European countries, only Sweden and Germany have a total ban on all forms of homeschooling. They should be fine in Portugal or can stay in Finland, where at least 14 other Swedish families have "fled" in order to continue to homeschool their children.