@jespah,
Jespah, I am guessing the the cousin is offering to pay the airfare difference for her to come down during a different time frame when she would be there. I'm reading it that way. Or as an alternative, she would keep the current ticket and come down and dog sit, which would be ridiculous for the OP to even consider.
That said, I think the cousin is at least being reasonable. She is recognizing that her change in plans to go on this cruise may create a financial issue for her visiting cousin and has made the offer to pay any airfare difference to change the flight to a different time when the two of them can spend time together. Yes, the cousin COULD have told this new guy that she could not go on a cruise that week, but we don't know the exact particulars and should not judge the cousin's actions too harshly. Maybe it is the only week the new bf could take. Maybe it was an already planned cruise that was past the final payment date and cancelling would have cost him a good deal of money.
Anyway, OP, get over being mad. In the big scheme of life, this ain't worth it. Have her pick a time after her cruise for you to come down and take her up on her offer of reimbursement for any additional cost incurred to change your flight. Go see her and have a good time. You'll even get to talk to her about how much fun she had on her cruise.