What features are useful on a bike for carrying children?
In the Netherlands something has evolved that is (unofficially) called the "mammafiets" or "mothersbike" main features that make it a useful bike for cycling with children are:


A larger distance between the saddle and the handlebars to allow plenty of room for a child seat on the handlebars.
Wider handlebars to make it easier to reach around the kid in the front-seat, and to make steering with a kid in the seat easier (more leverage) and the ride more stable.
A support stand that has feet on either side of the frame to make it more stable when parking
A steer-lock to keep the front wheel straight and stable when your kid is in the front child-seat when you park the bike (very easy when loading a second kid on the back-seat or when opening shed-doors, etc.)
A lower saddle to allow you to reach the ground more easily with your feet
A slightly longer rear luggage rack to give the kid in the rear-seat a bit more room, and still allow for panniers.
An extra low step-through frame.


This is a typical example: