You're in a sticky situation there. Your cousin did get the permission and you are technically a guest of his on the property so you are at his mercy. I can't say I agree with your cousin on that aspect of not allowing you to shoot the big deer if provides you the opportunity to me that is selfish and rude. It is not like he's been hunting this deer perviously no time or effort invested in this animal. As far as dividing the friendship goes his comments have already started that otherwise you wouldn't be on here asking for advice. And no that is not how it really goes when you hunt with someone on their land. I no longer have any private property to hunt but when I did the rules were simple we only took the animals that the land owner said we could (which in most cases was any legal deer), I had a rule on bucks that we didn't shoot them unless there were something we were going to put on the wall (no reason to go shooting all the small deer). There were no animals that I would say you couldn't hunt because they were mine. Hunting seems to be 50/50 Hardwork/Luck.

IMHO Your cousin is not in the right but its his sandbox he's just letting you play in it. Good luck and Good Hunting!