This sounds like you're wrestling with your pride/ego.
Allow me to get pseudo philosophical right quick:
In instances like this (and eventually your marriage) there's going to have to be some surrendering. But don't understand it as surrendering to a person, see it surrendering to a concept; in this context, the unconditional love between son and father. Much more important than your "ego", yes?
To that point, surrender to love, not your father, and sit at that table, even if you're unsure he'll join. Do what you can do to peace it up. If anything, you'll feel better knowing you tried.
Invite him. If he doesn't meet you there, you did your part.
This is where ive been the past 6 months, and he has not come to that table. I wont be here forever. I hear you, i really do, but i have to be the man in my family, i can't remain the child in his forever
a nikka couldn't leave the house for an event outside of the school till my graduation and even then, she was waiting to pick me up like I owed her money.
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for being a stand up breh