There are several pages about building kids trailer:
New EU Standard EN 15918:2011 for Bicycle Trailers
There is mentioned EU standard:
A voluntary European standard (EN 15918) for two-wheel bicycle trailers was published in September 2011.
This standard applies to trailers carrying cargo and/or up to 2 passengers, and enforces a maximum gross weight of 60 kg. There are many safety-related requirements, including restraints, structural integrity, stability, small parts, sharp edges, etc.
You should check if your country has national regulations because they supercede EU regulations.
My toughts about design process:
You can make 3d model using software like Solidworks and also run structural anlysis, check stresses and deformations. Maybe use parametric model and later optimize construction when you see stress profile. Also check available materials, aluminium alloys are used often for bikes, light and not as expensive as carbon fiber, shaping and connecting parts may be problem with sophisticated materials.
Stability should be also your main concern and I would advise getting this EU standard.