German Child Support

Hello everyone, 

A quick background: I became chronically ill in 2020 and have been battling with illness ever since. I have two children with a German national, they were both born in Scotland, I never lived in Germany and I am not married. 
 

My partner (ex), went on holiday to Germany with our two children in 2021 and never returned. she is there without my permission and has vowed not to return to Scotland. 
 

She has been receiving child support in the form of Advanced maintenance payments from the German government, and from what I can understand I am responsible for paying this back to the state. 
 

I haven’t been able to work since 2020, and my income (benefits) is so low that the German state has said I don’t have to contribute just now. 
 

My main question is am I responsible for paying back the money that has been advanced to the mother of my children? From what I understand, she will have received approx 10000 Euros thus far, 

My plan is to move to Germany when my health improves. 
 

Any answers or guidance would be gratefully received