Living in a city in Germany, a lot of families cycle with their children. Typically babies and young children have a seat on the handlebars or in a small trailer on the back, older children either have a tandem-style attachment or their own bike. The various attachments are typically fairly generic, so should work for both regular and electric bikes.
You can also buy (or rent) tricycle-style bikes that have a large space at the front to carry heavier loads - children, pets, or just shopping. I assume there are electric versions of these as well.
In fairness, most of this assumes that the city is reasonably bike accessible, mainly in terms of having all the necessary amenities within a cycle ride from home. If you live in suburbs, this may not be as possible. But I think that says more about the inadequacy of poorly planned cities than that of electric bikes.