So easy child stole the firecracker, not difficult child? I would tell difficult child that I am sorry I accused her and I know she didn't do it. I would NOT attach the "but your past actions mean that I cannot trust you so you are going to be the first one I think of when a problem happens." That part will just cause bad feelings. The unconditional apology will model how apologies should be made when you make a mistake.
easy child 1 may have been through a wringer because difficult child's actions. How does that have ANY bearing on the fact that he stole something? Just because they are pcs and have a harder time does NOT mean that they should not have logical consequences whey they do something wrong. Period. difficult child koi has no real connection to easy child stealing, unless difficult child told/convinced/forced easy child to do it.
If you let easy child off the hook you teach him that it is OK to steal if someone in your life is hard to deal with. Do you REALLY want to send that message? You could grow a difficult child out of your easy child if you don't treat his mistakes with logical consequences. That would make life much harder for the whole family.
My kids were taken back to the store to confess and to give the item back. They also had to pay the full price plus tax for the item. They did NOT get to keep it. So far no one has ever pressed charges but that is their right and a consequence that easy child would have to face. Many managers/owners are just thrilled to see a parent who is not ignoring it or encouraging it, in my opinion.