Diatoms reproduce by separating the two halves of their shell and regrowing a new half. It seems to me that it would be difficult to predict the shape without an existing half shell. If anything, the shape is probably mostly determined by the shape of the existing shell; if a parent is damaged and a chunk is missing, you want to make a new half shell that seals up against that half instead of the shape it's "supposed" to be.
I think you're right. The DNA does control the shell shape, but the way DNA works is always thru chain reactions (secondary effects) rather than something akin to a blueprint of any kind. So if you took out the DNA and put it in the "wrong half-shell" (using your concept), I bet it would be unable to complete the other half shell that looked symmetrical, and I bet it would die, because without the symmetry it cannot "complete" the shell, and the outside environment would therefore seep in, corrupting the cell internals, and it would die from that contamination.
