Your questions may be confusing your enquiry by too closely comparing DNA-based life and nanotech. Although they both operate at a nanoscale to create much larger objects they are very different in approach.
DNA is the end result of many trillions of random events. Various simple molecules that tended to create more of themselves eventually resulted in more complex chemical mixtures that eventually resulted in the first very very basic cells and the resulting explosion of activity we call "life".
In the same way that you would not call a tree blown down across a stream a "designed, engineered and constructed" bridge you cannot compare DNA with mature nanotech.
Even basic nanoassembler doesn't exist yet because the engineering techniques have not progressed that far.
There will be limitations on what can be created but they are not in the direction you are wondering about.
Mostly they will be related to the physical limitations of molecules. They can only withstand so much force/heat etc before changing their structure. Heisenberg's uncertainty, like all physical laws, will of course apply but that law doesn't cover large scale uncertainty such as the twins. It effectively covers utterly tiny quantum events (well below the nano scale but still possible effecting engineering of it.)
The limitation I believe you are interested in is the complexity of the object created.
A life form is highly complex (once built) because of the vast chaotic detail within it.
This complexity would require vast computational resources to analyse and reconstruct.
Compare that to using nanotech to build a kilometer cube of diamond. The instructions for that would be simple enough for a child to memorise.
Note that the DNA molecules themselves are relatively simple compared to the entire adult organisim.
Note that the vast computational resources required to handle the design of lifeforms (particularly their brains) may be available if nanotech is used to build extremely powerful computers.
Practically every large science research group is involved in nanotech.
Current research has a long way to go to get to the stage of Drexler style mature nanotech. Most research these days is around using techniques such as molecular chemistry and integrated circuit technology to create very large volumes of material which has nanoscale features. Microelectromechanical systems (MEMS) is also a promising area.