Can I seek full custody of my children after our divorce if I can prove my soon to be ex husband is an irresponsible parent?

The matter of child custody is determined by the local courts of your state that deal with family law matters.  While both parents typically have rights to their children after a divorce, the court may deem one parent the custodial parent, which is essentially sole child custody.  If you are successful in persuading the judge that you should have sole child custody, or if your husband agrees that you should have sole custody, you will be responsible for all decisions and care related to your children.  However, even if you do get sole custody, your husband will still have parental visitation rights.  You should also know that if your husband objects to you having sole child custody, you will have to rebut the automatic presumption that joint-custody would be in the best interests of your children.