If you or your children cause any sort of damage in a private context or harm somebody, you are normally held responsible for all costs. In that case it is irrelevant whether is was on purpose or a misfortune. In order to avoid that, it is highly recommended to have a liability insurance. This insurance is no mandatory insurance.
Possible German insurance companies are HanseMerkur, BavariaDirekt, LVM Versicherungen and Gothaer. If you are looking for an insurance that offers English speaking service, you might also want to have a look at Vela.
Additionally, you can compare various offers and choose the one that fits best for you on Check24.