Dear Lydia,
Welcome back to the Wefugees Community and thank you for being such an active member!
I wanted to share with you the information that there is an option to make a "Teilzeitausbildung" (vocational training in part-time) which allows you to actually start a training even as a single mother. I highly recommend to get some individual support in a counselling office. They can help you searching for an appropriate vocational training place, praparing your application documents and may also be able to help with child care questions.
I hope this helps and please don't hesitate to get back to us with any further questions or if you need help with finding a counselling office in your area.
All the best,
Meike