Integration courses are offered at every adult education centre [Volkshochschule] in Germany. Many also take place online. You will find information about this here.
You will also find information on the websites of the respective federal state and social welfare offices. Here for Leipzig, for example.
An example of an integration course with childcare can be found here.
You will find language courses specifically for Ukrainians from the Mitteldeutsches Institut (MIQR) here.