Even before I read any of the other posts above, I was surprised to read that you got "very angry" at your brother's response. He is putting plans he made for his immediate family over plans you've just made for your immediate family. That strikes me as okay. I think you've already created awkwardness by suggesting he shift dates around to accomodate your plans. His note to you already tells you that he is prioritizing his own plans. Your request that he consider shifting his rental dates is you trying to pressure him. He probably resents that, which is why he has not responded to your 2nd note. He would be well within his rights to not respond further. Your second note, actually, was not polite IMHO. It comes off as an attempt to embarrass him.

Would you really want your daughter to be surrounded by people whose arms you twisted into being there. How embarrassing for her that would be, if she knew.

I won't say you're wrong to feel "very angry" because we don't choose our feelings. They simply are what they are. I do think you would be wrong to let your brother "have it." You can't guilt relatives into having warmer feelings toward your daughter and you. The effect will be the opposite. He may, indeed, have very warm feelings for your daughter. That doesn't obligate him to show up in person for every milestone she hits. Almost everyone in the United States graduates from high school. No one is socially obligated to attend every graduation of every niece and nephew. Your expectation strikes me as abnormal. That probably is symptomatic of a larger issue you have that you believe no one is allowed to disappoint you. Maybe you just apply that to relatives. Your defense is that "Family should come first!" Few will argue against that. However, the family duties of an uncle are not at all the same as the family duties of a father. If they were, we'ld all be crushed under the burden of family duty.

Celebrate your daughter's achievement with a joyous get-together of those who are there because that's exactly where they want to be. Maybe it will just be your immediate family going out for dinner at someplace elegant. That would be perfectly alright as an option.