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You have a good chance of getting placement of the children under the above facts, but there are other considerations. Your wife, while being neglectful, has been the children's caretaker while you are in the military, and the courts look at that to determine physical custody.
Also, since you are still in the military, the courts will wonder who will care for the children while you are working, or possibly even deployed again.
These are things you will have to work out before your final court hearing on custody. But, I think you have a good chance. Remember, however, that the court will likely not talk to your son under any circumstances. Call your wife's boyfriend as a witness and he might tell more than you expect.