Is God's will ever evil? If not, then his will is not always done because evil is always done. Was it God's will for our twins to die (People can substitute most any tragedy in their lives here). I don't think so. Did he allow it? Obviously, he did. Just because he allowed it, doesn't mean that he willed it.
Just because I allow my child to do something doesn't mean that it is my will that he does it. I might be waiting for him to make that mistake in my presence so that I can correct him. My goal is that he wouldn't make that mistake ever but always choose to do what is right. I want my child to grow up and make the right decisions. In order to do that, I need to allow him the opportunity to make the wrong decisions.
God made us in the same way. He could have made puppets that always did his will. For some reason, that isn't what he made. He made people that can choose what to do. He would prefer for us to make the right choice; He could even force us to always make the right choice. But he chooses not to. That doesn't mean that when we make the wrong choice and bad things happen that His will is being done. It means the exact opposite. It means that we made the wrong choice.
Not only do we suffer from the consequences of our own wrong decisions. We live in a world that has consequences abounding from people's wrong choices. Not only do we suffer for the wrong decisions of those around us now, but we also suffer for the wrong decisions people have made in the past.
A world without suffering and doing wrong would be a world void of free will. For some reason God chose free will to be the priority.
Because of His decision to give free will, God is left with the same role that we have as parents. We could force our children to do what is right, but that really wouldn't matter in the long run. What really matters is training them to choose to do His will all of the time. That is what God desires.
I think in discussing this we morph various questions that should be dealt with separately.
"Is God's will always done?" I would argue absolutely "no".
The other question is: "When God wants to force His will on humanity can it be thwarted?" And I would argue absolutely "no". His forced will is irresistible.
Is God accountable for not intervening when He doesn't force His will? I would say that He is, but as He explained to Job, we don't really see the big picture and realize totally what He is trying to accomplish. But that doesn't mean that when He doesn't force His will that His will is being done.
He gave us free will but it is not His will that we make the wrong decisions.