All images print with too much pink

Could you please be more specific as to where your images are coming from in the first place and exactly how you are exporting them? If the images are coming from Photoshop into InDesign and then being exported to pdf to be viewed in Acrobat then it is essential that the color profiles in both Photoshop and InDesign match. You can do that by going through Edit>Color Settings in both programs and choosing the same profiles for each. With the color profiles so aligned there should not be any further problems with the colors of the exported images.

Where are you seeing this? On screen - in printed files?

InDesign has it's own colour management system

And your photos will have colour assigned to them.

Copying them to Word would convert them to a different colour space.

If it's Acrobat that's not looking correct, then have you colour calibrated your monitor?
What colour profile are you using to view the images in Acrobat.

https://helpx.adobe.com/ie/acrobat/using/keeping-colors-consistent.html