Sounds like Corel doesn't support live transparency effects in a PDF. So
try flattening the PDF during export in InDesign.
(Try using the PDF/X-1a:2001 preset.)
So, if you don't want to edit, what is it you need to do in Corel Draw that you can't do directly in ID to hand off for printing?
Sounds like this is one of those off-shore oddball printers that want CorelDRAW files. I didn't think there were any left. That said perhaps the OP misunderstood and they ACCEPT CorelDRAW. I would certainly do all I could to contact the printer to get this clarified.
There's nothing to be gained by taking that ID file and putting it into CorelDRAW no matter how you do it.
Adobe and Corel products handle effects (like blur, or dropshadow, or even gradients) completely differently from each other. The only chance of having them move from one to the other is to rasterize any such effects before making the PDF (DO NOT save this over your original file!).
Note that I said it's a chance. Even these will be mishandled from time to time.