I would never go with my kids on a bike on any road that's shared with cars. The risk, as small as it is, is still unacceptable to me.

Don't know about Germany, but in Netherlands it's solved with having proper cycling infrastructure. It's the right approach, but it is still more of an exception. Where I am at they just painted cycle paths on existing roads and then tried to make it safer by cutting speed limit in half and eliminating lots of street parking. And now it's a mess that doesn't work well for anyone. Next elections are in a year, will be interesting to see how that will go.