It sounds to me as though both little boys might have some real emotional problems. I would begin with their mother. It might be difficult for her to arrange to come in and talk with you while you have responsibility for the children (perhaps at naptime?), but I would insist on it. Make clear to her that you are not blaming her for the behavior and that you feel that working through it will require a joint effort from both of you. If she refuses to meet with you and to try to work out a helpful plan of action, let her know you can't keep the boys any longer.
But now, while they are with you, vigilance on your part is very important. Try to learn to anticipate when a tantrum is going to occur (the signs are not too hard to read) and distract him. Offer a new toy, move to a different room, read him a special story. And be sure to praise him whenever he handles a difficult situation without a tantrum.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.