Dad's girlfriend invited to our wedding?

Hi,

I have a dilemma that keeps me up at nights. My parents divorced more than 3 years ago. In a half a year after that, my dad started living with his new girlfriend whom I really like and we meet often all four with my fiance and spend time together.

My parents are in good terms, they sometimes call each other, tell how is it going and so on.
My mum doesn't have a boyfriend.
I now wonder if I should invite my father's girlfriend to our wedding. If my father goes alone, there won't be any other people from his side, except me. So he won't have a good time for sure and will be upset that I didn't invite his significant other.
If father's girlfriend will go to the wedding, my mum might feel really upset and uncomfortable, eventhough she assured me she will be fine. I just know she is a sensitive person and might not say how she really feels.
Maybe you could give me some advice?
It's so hard to keep everyone happy..