I've not got clear understanding from what you posted about when you are seeing this maximized window when the software opens? When running in real DOS, there is no such thing as a window.
Why not just start your computer up in DOS mode manually, and start the program from a command prompt? All you need to know is the path to where the exe file for your program is located, and DOS, properly set up with config.sys and autoexec.bat files should load it up. Keep in mind that DOS file names cannot be longer than 8 characters, and a long filename is truncated with the '~1' or '~2' on the right end, before the file extension.
IIRC, I think Windows could be configured so that it would rename the config.sys and autoexec.bat files automatically. This is because these two file names have 'magic' associated with them, and your PC will run those files first whenever it boots, if it finds them, and then windows itself may not load properly. So when Windows is running, then config.sys needs to be renamed to config.dos and autoexec.bat needs to be renamed to autoexec.dos.
When in DOS mode, those two files must have their extensions changed back to the .sys and .bat so that DOS recognises them. Of course, these two system files should also contain some information and not just be empty.