“My wife has been cheating on me, and I think she’s an alcoholic. I want to leave her, but I’m worried that I won’t get custody of our kids (ages 6 and 8). Are the courts still reluctant to grant sole custody to fathers? How can I increase my chances of getting full custody of my boys?”
The smartest thing for you to do is to continue to parent your sons. In other words, DO NOT LEAVE. If you feel that it is necessary for you to live apart from your wife, take your children with you. (There are also financial reasons why you should not leave your home.)
However, since you are simply preparing a divorce at this time, it may be a good idea for you to get your wife help with her alcoholism. Therapy and/or alcohol counseling will do one of two things: get her help which will save your marriage (which you may or may not want to do) or build your case for custody. Although there is often a doctor-patient privilege with regards to this counseling, that legal privilege (a therapist would not ordinarily be able to divulge representations made by your wife during the course of counseling) is not adhered to when custody is at issue.
The primary concern of a court rendering a custody determination is the “best interests of the child (or children),” and courts are reluctant to exclude any evidence that would bear upon the best interests determination. Courts are not as reluctant as they once were to grant sole custody to fathers. In New York and New Jersey, there is a “gender neutrality” with no presumption that either parent is a better custodial parent than the other, and this applies regardless of the age of the children. (Were your children older — say, teenagers — their wishes would be controlling. The relatively young ages of your children will result in their preferences being heard, though not determinatively.)
While your wife’s marital infidelity is top-of-mind for you, it is an emotional concern with little relevance to the issue of child custody. The only possible impact of her infidelity on the child custody determination would be if she has introduced the new man (or men) into the lives of your children, or if this new man was a child molester.