ssjtrunks to the rescue! First of all, you use the destruction sphere in Bevelle temple no matter what because you have to(that's one less thing for you guys to worry about
). Second, I have yet to see a Final Fantasy game where if you don't do something that you can never have another chance to do it and you'd have to start a new game. Finally, you need to get through the door in Remiem Temple and here is how:
You need to defeat all of Belgemine's Aeons, except for Anima and the Magus Sisters, and you get one of the items you need to break the seal. To get the other one I believe you have to find all the monsters in the calm lands and capture at least one of each. DOing this gets you the final item you need to break the seal in front of the magus sisters. To do that just go up to it and the items will be used automatically, enjoy.
