Bless your heart. You have been handed a hard burden here. I am so sorry that this has come to light because any decision you make will be a hard one.
Sometimes God hits us in the face with realizations of what we should do in our lives. Those are easy. (Well, the knowing is easy. Sometimes the doing is hard!) Sometimes He speaks to us but we don't understand the meaning. And sometimes God shuts doors so that we don't do what we are looking for guidance on. The first and the last ones are the easiest for us. But sometimes God doesn't make things easy.
I personally think that maybe the 2nd scenario above is what might be happening here. (Not a religious inspiration - an impartial view of a 3rd party.) Your older boys are giving you so much trouble, which will undoubtedly cause their youngest brother to continue the pattern if you are not able to get them enough help. You already know this, but perhaps God expects you to use this knowledge to save that little girl from this family dynamic away from her brothers' problems. Perhaps you could look at it this way - if she is adopted into a family without problem children, she has a chance to blossom and flourish because she hasn't been with her mother long, like her brothers obviously were. And she wouldn't be exposed to the brothers' behaviors which will undoubtedly affect her in negative ways.
Another way to look at this, is that God may want you to focus on these boys - the baby will take a lot of time and effort, which takes away from the boys. Boys have so many strikes against them in this day and age - boys in the situation you have brought them out of are at-risk - they need every effort to help them stay out of trouble when they become older. That means you expend every effort on them now, while they are little, so you have a chance of helping gain control before the adolescent hormones kick in. Regular teenhood is hard enough - I know - I have two teens myself! Children who have been abused or neglected, as it seems the boys were, are at risk for alternative school, juvenile court, and worse.
Please think about what I have said. A calling is admirable, understandable, and society owes a lot to those whose callings help society in real and tangible ways. However, a calling should be tempered with knowledge, understanding, and good common sense. There's a point where you should stop and put your energies of that calling where you are now - which means not taking on more.
All my best to you, and my prayers are with you to make the right decision.