(I'm french so sorry for my poor English)

I think the best way to teach Euclidean space to children is to just make it simple:

Two parallel lines will never meet. Like on a map that you can show them.

Then the best way to explain a non-Euclidean space to children is with a Earth globe. You show them the meridians and the longitudes. How the meridians are meeting at the poles even if while watching outside, the Earth seems plane. The globe is the best thing to explain that to a child I think. Just put his finger on the North pole.

How could you expect a child to understand that a triangle doesn't have 180 degrees of corners in a non-Euclidean space ?

Maybe i'm too simplist for you but that's what I think.