File type color change

After creating a design with a transparency effect, and a black background under it, I save it as cdr and then export as png. I used cmyk during design. The black turned out about 85% black and the transparent glow effect seemed to run the whites together and the text was not readable as it is when its cdr. I thought saving in png which only uses rbg, would result in an accurate conversion of colors so that what I design and what I print are almost identical. 

Should I design in rgb? Is there some other way to convert the colors so that when it goes to production it won't lose color? The printer really only takes png. I'm not sure why since png was for transferring digital images to screens and not meant to be printed. I'm just stressed out over the color differences. Black should be black no matter what file type it is, right? 

The white glow seemed to expand. Its not just the printed version that's obscure. Once exported I can open it in any other picture program including on my phone and it looks no where near the actually design. Is there a magic fix our plug-in I don't know about to resolve this issue?