If my wife and I are legally married but she left me and moved in with a married man, could I get custody of our 3 year old?

The fact that she moved in with a married man-- or with another man in general-- is a factor that the court will consider in deciding child custody.  Many judges frown on the having a child in the house during an extramarital sleepover.  However, it's not the only factor.  The court will look at a variety of factors to decide what is utlimately in the best interest of the child.  Instead of banking on this one factor, you should also be prepared to show the judge why your household would be better or more stable for the child.  Factors could include being able to provide the child with a room of their own, that you have access to insurance benefits, you are located near better schools or educational programs, you have quality child care, or you have family members close by to give the child a sense of family and help you raise the child.  This is not an exhaustive list, but it demonstrates that you are concerned not just about punishing your ex-, but you're interested in being the best possible parent for your child.  Considering that your child is very young, the more factors you can show, the better the chance you'll have at getting custody.  A two prong approach is much more effective.