There is an issue when ChemDoodle and JSmol are instantiated on the same page. I don't know whether this is a bug in JSmol, or a bug in ChemDoodle, or some incompatibility that is not a "bug" at all, but here is the problem regardless.
ChemDoodle can write a data file in MOL format and that usually works fine. However, when JSmol (13.3.9) is running in the same page (under several Mac and Windows OSs), the MOL file generated by ChemDoodle is lacking key data; several fields contain "undefined" instead of atom numbers, etc. Since JSmol cannot (currently) import the native ChemDoodle data format, the problem with the MOL file means that molecule data cannot be transferred between the two applications. Transfer using SMILES, and other data formats, is possible in principle, but requires "Cloud Services" from iChemLabs (the creators of ChemDoodle), which users may not have.
With thanks, Mike.