if image is CMYK and transparency blend space is set to CMYK in Indesign--try this export as PDF using high quality print preset--then try printing the PDF--also try opening original image (if PSD) and resave as flattened tif (change name so original remains intact)
but based on " Funny thing is that when you take that same file and send it to another printer, it prints accurately." there may actually be a problem with the 'new' printer