Does "女朋友" work for older couples? I'm going to be visiting China next year, along with my father.  My parents are divorced, but my dad is now dating someone who will likely be coming with us.  They aren't married, so I'm not sure what word to use to introduce them.  If I say something like, "这位是我爸爸，和我爸爸的女朋友", would that cause confusion?  Is there another word for this, or would something like this be uncommon in China?
Using archaic phrases like 红颜知己 or 忘年之交 is a bad suggestion, these phrases come straight from dated Chinese movies. No modern human talk like this in real life. It is like saying " She is my father's fair lady" or " she is my dad's dear confidant." in English.

If they are very close, saying she is 女朋友 (girl friend) is perfectly fine in today's open minded society. 

The safest option is to call her your dad's 朋友 (friend). or 好朋友 (good friend) if you are not sure they are officially a couple or not.