How can we prevent others (printing press) from reproducing our designs/layouts after we submitted our soft copy to our clients?
Until now, I only submitted hard copies, provided that we can easily submit via email the soft copy.
You can not. Its technically impossible and requires future tech that is not even available for the NSA (if it was then no edward snowden). You can however degrade the soft proof so that it is nonsuitable for use in print (export as low res bitmap). This does not stop some entities apparently.
So the real answer is you stop this practice by writing a contract. If you do not trust your clients then you should not have them as clients.
Before sending your pdf to the client, go to: File > Document Properties > Security > Security Method: Password Security. Once you turn on Password Security, you have the option to restrict editing (none) and printing (none or low resolution). You can even disable copying of text, images and other content.
Why do I get the feeling you want a James Bond file that self-destructs in a relatively small period of time after the user has opened it? [joke]
If you are having trust issues with your customers, you could [this assumes that you have a website] :
This way you may have some control and really make the image unavailable after 10-30 minutes after he logged in to see it. If you are lucky enough for your customer to use an updated browser you can even disable print-screens and right clicks but :
Export the layout/design not as an image but rather save it in pdf format. If you are using Illustrator, uncheck the Preserve Illustrator editing capabilities so that it can not be edited in ai as well.