Actually, no that i have re-read the entire thread, I think that I am going to change my advice... everything else aside (pretend that your father does not need you to be his chauffeur) ... would you want to go to this birthday party?
I was struck by something that the OP said in the resolution of the original thread - "I did also make it clear to my father that he was not to ever call a relative again looking for an invite for me so he would have a ride. I also told him that if I started to feel like I was only being invited someplace just so he had a ride I would not be going."
If you want to go, for you, then by all means go (and take your father) and bring whatever card or level of gift you feel like bringing.
If you really don't want to go... then don't go. Decline the invite. Let the cousins come and pick up your father. They did it before and if they really want your father to be there then they can do it again.
I agree with all of this.
IF you can set aside the past, just for a moment, ask yourself how the invitation makes you feel. If it's anything less than excited, or at least 'Oh, cool....a party! I get to reconnect with the family!', then when you add in the past chauffeuring incident, then I'd say that yes, you're probably being invited for a ride.
Look, everyone involved is an adult here. They're obviously capable of figuring things out, like the fact that if they want the OP's dad there, then he has to ride with someone. And since this is a party, he has to ride with someone who was invited. So presto....that means an invitation for the OP!
I guess if you really want to find out where you stand, could you take the ride out of the equation? Is there any way that you could go to the party, but be unable to get your dad? Might you already be in the area of the party so you can't backtrack to get him, or would you have a really tight schedule so you can't afford the extra time it would take to go to his house, wait for him, etc.? Could you take a train? That way, if you're not giving him a ride (the supposed 'purpose' for the invite) then you can find out of the invitation is a sincere one or just a means to an end for them.
Even if there's nothing else you can do, I would NOT mention the party to your dad. Let THEM (your dad or the cousins) bring it up. Make THEM ask you for a ride for your dad. And if your dad does any sort of assumption about you giving him a ride, then I think you have your answer. Even if he knows you were invited, just that is somewhat telling, because it means that your invitation was brought up to him, and one can extrapolate that it was brought up b/c of the presumed transportation issue.