Hey, this is my version and hope someone can help you make it even better.
Thank you for inviting me to your birthday party.But I am really sorry that I can't go. My brother who stays in the U.S. will be back home tonight. My parents and I will pick him up from the airport. I miss him so much cause I haven't seen him for a year. Basically this is why I can't go to your birthday party. Though I can't go, I'd like to give my best wish with all my heart: Happy Birthday!!
PS: If you can still prepare a birthday gift for him or her, it would be really nice.