Bonyk, have you tried asking Older Cousin why she won't let you pay a share? "I just don't get this. I thought we all agreed that we were buying Grandad a Freestyle Clockwatcher between us, and now you're saying that no, it's just from you. Why have you changed your mind?"
And if she says that no, it's just that she can afford it, point out that so can you. Sounds like you may need to say out loud in real words "I'm all grown up now, I have a job and an income and if I couldn't afford to buy my share of the present, I wouldn't have suggested it in the first place. It was my idea, remember?"
Possibly if you make her express her reasoning out loud she'll make more sense.
Possibly not, but worth a try, I would have said.