People with disabilities have a legal entitlement to a so-called "personal budget", which is paid to them instead of service or in kind. This allows them to independently finance benefits that they need for daily help, and thus make their own lives. Parents of disabled children are also entitled to a personal budget. It can be used, for example, for individual help, social assistance from the youth welfare office or holiday care from the youth welfare office.
Information can be found in the brochure My child is disabled - these aids are available http://bvkm.de/wp-content/uploads/2016_Mein-Kind-ist-behindert-diese-Hilfen-gibt-es.pdf
https://www.elternimnetz.de/kinder/sorgenkinder/hilfen.php#5
An overview of the benefits for disabled people can be found here: https://ms.sachsen-anhalt.de/themen/menschen-mit-behinderungen/rehabilitation-und-teilhabe/eingliederung-sozialhilfe/
The social welfare and youth welfare offices provide help.
An overview of organizations and foundations that support seriously ill and disabled children and their families is given here: https://www.myhandicap.de/recht-behinderung/finanziellen-hilfe/kinder-jugendliche/