I know of 3 men who live in my small town who have 100% custody of their kids for reasons not even as bad as your situation. Unless you have some history that the courts would deem you an unsuitable father, your future lies in 1. raising your toddler or 2. losing your toddler to foster care or worse. Your wife is going to lose custody of her child, and if you don't make that happen, some other authority will. So you need to make it happen on your terms.
BTW, the dads I'm referring to: ALL their kids (all girls) are good students, active in a lot of activities, and have an excellent shot at living a happy, healthy life. While raising a kid alone is not something dads sign up for, most do fine when forced to rise to the challenge. Your life is about to drastically change because you're going to make a change. Embrace it and I wash you all the luck in the world.