The Court's Position
Family laws are not universal -- they vary from state to state -- so your situation may be more bleak in one jurisdiction than another. For example, Illinois statutes focus almost entirely on whether the custodial parent – your spouse – is alive and fit. If she is and doesn't want you to have time with your stepchildren after your divorce is over, you probably won't have visitation or custody.
Other states, such as Florida, will allow you to ask for visitation with your stepchildren as part of your divorce action, even if your spouse objects. Whether the judge grants your request depends on your relationship with the children, and whether the judge believes an ongoing relationship with you is in their best interests. If you were close and an integral part of their lives, there's a chance that the court might override your spouse's wishes. This assumes that she has custody. If her ex has custody, you may have to file a court action against their father, separate and apart from your divorce. You may not have this option in some states, so consult with an attorney.