Dear Really Motivated,
Welcome back to the Wefugees Community and thank you for your question.
I assume that your children might be entitled to receive a residence permit according to section 25a of the German Residence Act as "well integrated juveniles"?
(1) As a general rule, a juvenile aged 14 to 18 or a young adult aged 18 - 21 whose deportation has been suspended is to be granted a temporary residence permit if
1. the foreigner has resided in the federal territory for four years without interruption either by virtue of holding a temporary residence or permanent settlement permit, by virtue of his or her deportation having been suspended or by holding permission to remain pending the asylum decision,
2. the foreigner has successfully attended school in the federal territory for, as a rule, four years or has acquired a recognised vocational or school-leaving qualification,
3. the application for the temporary residence permit is filed before the foreigner reaches the age of 21,
4. it appears, on the basis of the foreigner’s education and way of life to date, that the foreigner will be able to integrate into the way of life in the Federal Republic of Germany and
5. there is no concrete evidence to suggest that the foreigner is not committed to the free democratic basic order of the Federal Republic of Germany.
For as long as the foreigner attends school, vocational training or higher education, claiming public benefits for the purpose of ensuring his or her subsistence does not preclude the granting of the temporary residence permit. A temporary residence permit is to be denied if deportation has been suspended on the basis of false information furnished by the foreigner or on the grounds of deception by the foreigner as to his or her identity or nationality.
It might be a bit confusing but Section 81 (1) is a very general held section saying:
(1) In the absence of any provisions to the contrary, a residence title is issued to a foreigner only upon application by said foreigner.
Therefore, the application of those two laws are not excluding eachother - it is not an either/or.
Did I get your situation correctly? Please don't hesitate to get back to us if clarificaton is needed or you have any further questions.
All the best,