I don't know any of the details, but since you say it's your brother's wedding, let me give you a bit of advice before anything else: you can either participate and experience the wedding, or you can photograph the wedding and have no memories of the event afterwards. When covering the ceremony, the photographer is literally lost in the moment, concentrating on getting the photo, and I remember no details from the ceremony. As his brother, you may not be comfortable missing out on that.
In any case, weddings basically require a flash, and renting a Canon Speedlite is unavoidable (in my opinion). No matter how fast your glass is, it's never enough light. Even outdoors, you'll want the flash as a fill light for shadows and balancing against the sun.
In regards to the other equipment you list, the only think you're missing is a wide angle lens, such as the EF-S 10-22mm, which you'll probably want for group photos.
Everyone's method for shooting weddings is different, so you're likely to find as many different answers as people answering, but any more information about what the ceremony and reception will be like will help us guide your answers. Weddings happen in all forms, times of day, and places, and all of that plays into what equipment to bring and what photo styles you can use.