Just of note, the "drawing_units" option in the drawing properties doens't change a dimension from mm to inches, it changes the text heights (and other drawing parameter units) to mm or inches.
Obviously missing something and without the actual files, it's difficult to troubleshoot. So let's do some random troubleshooting.
In the problem part, go to the analysis tab, select measure and select and edge. You should get a length that says inches? Hopefully. Just making sure part is in inches. If not inches, part units are the problem

Create a NEW drawing (if you have template options, make sure you pick one that uses inches), with that same part. Make a view, add a dimension. Dimension showing in inches or mm? If the units are MM, drawing is the problem (or picked drawing template)
It really is difficult to show mm on a inch part. That's why Tom asked about dual dimensioning option. Its the way you can show mm on an inch part.