You can do it, but ...
It is easy in a desktop publishing program, but since you are probably using Word, it is more difficult.
If you are producing text that you are going to print on a typical printer, you can do it in Word by going through a somewhat meticulous process of "expanding" selected text. I am going to do this from memory, so you may have to work your way through it.
Basically, if you have:
"'Stuff.'"
To put some space between " and ' at the left of the word, you select (highlight) the double quote ".
Right-click on the selection.
Choose Font.
Advanced.
Spacing.
Expanded. Choose 1 point if it is not automatically chosen.
Okay all of that. It should put a thin space between " and '.
For the '" on the right side of the word:
Select the '.
Go through the same steps.
You have to select the " on the left side of the word, but the ' on the right side of the word. If you do not do it correctly, you get expanded text where you do not want it.
Are you really sure you want to do this?