Hi Wondering, I think maybe you have got two words mixed up - intervene and intercede. Intervening is what God does (or doesn't do) and interceding is what we do when we pray for people (and what Jesus and, if you're an RC, the Blessed Virgin Mary and the saints do on our behalf). Intercession is asking God to do something.
I think that God never does something directly that he intends to accomplish through human beings - though of course, we are free to go against what his purposes.
The way I think of it is that God holds all the possible outcomes of all the actions of us all, and works his purposes out in an infinitely slow and patient way - we can't see the patterns, because they're so much larger than us and so much longer-term than our individual lives; and we can't see how the pattern reforms after each of our actions; all we can do is to ask ourselves 'what is God's will in this situation? what would he want me to do? -- that's one of the purposes of prayer, to try and align ourselves to God's will.
I'm pretty sure that it isn't God's will that a child is abused. On the other hand, God made us in his own image, with free will. That means the freedom to do terrible things. And if God were to intervene to stop a child being abused, we wouldn't actually have free will at all.
It's one of those either you have it or you don't things you can't have free will only to do certain things. We have freedom to mess up big time which we do all the time. That's why we need Jesus, to mend our mess, to bring us back to God again, to take on our pain and suffering and to give us hope that one day all the mess, all the pain, all the suffering and injustice will be mended and healed and redeemed. When everything seems dark he's the light. And if it's so dark we can't see any light, he's the hope that somewhere there is light beyond the darkness.
And the Holy Spirit is there to pray with us, to pray in us when we pray; to be our comforter and guide, to help us to know what is the right thing to do, and to help us to do it. When we pray for others, one of the most important ways that God intervenes is to change us, through the power of the Holy Spirit, so that little by little we become the agents of the changes God wants to happen.
Someone said that praying is like getting a sun tan. You lie there, and you think you are doing nothing, and you can't see anything happening. But after a while your skin has changed colour. Prayer is like that: slowly, imperceptibly, it changes us (through the Holy Spirit), so we can go out and help to change the world.
Sorry, that was an essay!