From my (limited) experience, the texture handling capabilities of view3dscene and shapeways are about on par, so the error might be elsewhere.
That could suggest that something in the underlying geometry is wrong - degenerate triangles, tiny holes in the mesh, triangles with their face normal pointing to the wrong side (due to wrong winding order of cornerpoints). Shapeways' site software will try to fix any such problems and "repair" a model, but in the process it may add or remove vertices, which would then cause the texture to become misaligned. Unfortunately netfabb studio basic,
the freeware tool usually recommended for checking and fixing models, does not handle vrml. Can your software export to X3D (successor to VRML, practically same capabilities, just more XML decorations), which netfabb can read ? If not, try exporting the model to STL just for checking the geometry (this format does not support color or textures, but unless the problem is in the export module, any flaws should show up in the STL representation as well). If netfabb shows a warning triangle next to the model, you can run an "analysis" to get an overview of the flaws it found, and/or run various repair modes to reorient triangles, close holes or remove degenerate triangles (that have two or all three points identical). If that gets you anywhere, you can re-export the corrected model to STL and hopefully load that into your modeling software to reapply the texture.