Your dad is being very selfish about your special day! Whatever grievances he has with your mom do not factor in. Invite both of them and explain to your dad in a calm way that you wedding is about you and your future spouse, not his problems with the woman who bore you. If he cannot understand that, he is being very immature and should probably skip your wedding. Yes, not having your one or both of your parents at your wedding is not great, but neither is having a drama-filled day where all of the focus is on your dad and not you. Guests are invited to weddings to support and love the couple, not make it about them.
If you explain all of this to your dad and he still cannot act civil, then forget it. Let him stay home and miss one of the most important and wonderful days of your life. It may sound harsh, but you want to remember your big day as fun and romantic, not the day your dad pounded scotch and got in a screaming match with your mom over problems from 20 or 30 years ago. Keep your wedding about you—no one can fault you for that!