Which lens for pics of my children : Nikon 50mm f1.8g or 35mm f1.8g DX or something else?

Don't bury yourself under technical data which will lead to more confusion. Lens distortion is most of the times easily corrected in software.  Concentrate on your usage scenarios.

What settings of your 18-55 lens do you prefer for the portraits you are doing ? Look at all your pictures and find the focal length they were shot at.

If you're most of the time at 55mm, and like the results, then perhaps a 50mm prime lens is the one for you. I say perhaps because only you can know if you really liked that focal length, or sometimes wished to be further from your subject, but couldn't. As you noticed, longer focal lengths will often get good results for portrait. The subject is better isolated and the increased distance facilitates candid shots. For this you need a focal length longer than 55mm. I think you should consider the Nikkor 55-200VR. Cheap, good, versatile.