If I was to end up in a divorce and wanted full custody of my child, would it help in my favor if I had proof that my wife was cheating on me while married?

Under the laws of all states in this county the alleged infidelity of one spouse during the marriage does not have an impact with respect to custodial issues between the two parents pending the dissolution and afterwards. Given what you have written about I suggest that you consult with a family law attorney to assist you on your matter of inquiry.