If my understanding is correct (and i did read the whole thread) then this is what went down:
Summer/ early fall:
Dad says "let's do lunch at christmas!"
Everyone else, "Sure!"
Conversation ensues, the date is specified, but reservations are not made.
Another month or two goes by:
OP:" Are we still doing lunch on set date?"
Everyone else: "Yes!"
OP: "Has anyone made a reservation, or have a restaurant in mind?"
Everyone else: *silence*
Op looks at the calendar, realises set date is approaching, confirms date is still ok (affirmative from dad, silence from sisters), and knowing that reservations are booking up fast, calls and arranges a table for 5 at X restaurant on set day for lunch.
Op sends out notice that lunch is at X restaurant, reservation at Y time (probably 12:30 or 1?)
Dad replies "Great!"
Sisters say, "Oh, we just found out big family that dad doesn't associate with is on the same day. Let's cancel lunch and all go to that instead!"
OP says "We weren't planning on attending that."
Dad says "me either. But I will go with sisters after lunch if they need a ride."
Sisters say "No, no lunch, just big family do."
Now: to cancel or not to cancel. OP, I would ask your Dad.
"Dad, we aren't going to make it to big family do. We'd love to still have lunch on set day, but as we'll see you on christmas day, we'll understand if you want to cancel the lunch and just attend the big family do with sisters because of their schedule."
In my mind, he is the one that matters here. You don't really seem to care if you see the sisters or not (for which I don't blame you given the backstory) but given they ate going from big family do straight to Ma and stepdad's that may be the only time your Dad gets to see them during the holidays. He probably well knows that he won't get to visit them much at big family do, but it is what it is, and it should be his choice.
You and your DH have already decided not to attend big family do, I don't see why you would be expected to change that. In my mind, the only thing you have to decide is if you and DH are going to go for lunch by yourselves or stay home if your dad wants to cancel.