Divorcing the same man for the second time. is the original custody agreement still valid?

I would consult a family law attorney in your area. After reviewing all the facts of your case, including your previous divorce, the attorney can probably give you a more accurate answer.

My opinion is that the children still need to be listed and dealt with in this second divorce because they are still the children of you and your husband despite being born during your first marriage. Keep in mind that things changed during those nearly 8 years between your 2 marriages: financial, etc. So the child support will probably have to be revised to reflect your current situation.

As far as custody, if you and your husband agree on a custody agreement, you can submit it to the court. You can inform the court of your prior divorce and custody arrangement and state that the prior agreement worked well for both of you and it will be sufficient now.

Remember that the second divorce is separate from the first divorce. Just as you need to file new divorce papers, you need to file other new papers for this second divorce.