Hi @MIKE 130
As your partner has subisdiary protection in France, she cannot have a new asylum application processed in another EU country. The Dublin rules can allow for family reunification while an asylum case is ongoing but not once the person has been through the asylum process.   
You mention her having moved to Germany with her kids. If you are the parent of these children, then they can be issued with residence permits as your children. You will have to show you have sufficient income and living space for them and the mother will have to give her consent to them being issued with residence permits. This is according to paragraph 32, sections 1 and 3 of the Aufenthaltsgesetz: 
https://***.gesetze-im-internet.de/englisch_aufenthg/englisch_aufenthg.html#p0881 
A child born to a parent with a residence permit in Germany can receive a residence permit according to paragraph 33 of the Aufenthaltsgesetz: 
https://***.gesetze-im-internet.de/englisch_aufenthg/englisch_aufenthg.html#p0896 
I see no clear immediate route for your partner to receive a residence permit. The only option I can see is that the children are issued with residence permits and your partner receives a Duldung for family reasons. This would be a different type of Duldung than a ‘Dublin’ Duldung and after some time with this she could receive the permit 25,5.  
If you make an application on behalf of your children, it is important to point out that as they have valid residence permits from another Schengen country, this allows them to apply and be issued with permits in Germany. If you do not point this out, it is likely they would first be told to return to France and apply for a visa for family reunification there. The rule which enables a person with a permit from another Schengen country to travel to Germany and apply directly here is based on paragraph 39, section 6 of a separate law called Aufenthaltsverordnung: 
https://***.gesetze-im-internet.de/englisch_aufenthv/englisch_aufenthv.html#p0373 
A pregnant woman can be deported. The key question when it comes to deportation is whether a person can travel (in German ‘reisefähig’). There  is a period of time before and after birth when a woman is generally considered too vulnerable to be deported. This period is called ‘Mutterschutz’ and is 6 weeks before and 8 weeks after giving birth. Nevertheless, a medical examination may still declare a person fit to travel and in such a case a legal injunction in court would be necessary to stop the deportation.  
I cannot give any assessment on the chances of a person being deported or not. It is good to seek out information here and from other reliable sources. But we cannot offer legal advice here. You mention that your partner has a lawyer and he has submitted documents to the authorities. It is her lawyer who should be advising her on the possible options for her and/or her children to stay in Germany. 
Best, 
Éanna