The British company, Out 'n' About have a very popular (non running buggy). model called the 360 double which has many features of a running buggy EXCEPT the handbrake and the rear wheel being 16 inch. And obviously as it not designed for running with, any damage caused by running wouldn't be covered under warranty.
In 2016 they merged the design of their popular Single Nipper Sport v4 with their 360 double to create a light, fixed front wheel double running buggy. It has 16 inch wheels all round to provide a smooth ride and can fit through doorways!
Like all the Out 'n' About buggies, the Sport Double comes with a free rain cover so overall works out to be hundreds of pounds cheaper than the bike trailer option. It's very light (11.5kgs) which is always a benefit when pushing two kids and especially when steering a fixed front wheel, which needs lifting up. It's folds in half so will fit in most car boots plus has a handbrake to slow you down if needed down hill. At the moment it's sole colour option is in steel grey.