If we had children, can the marriage still be annulled?

Yes. One of the legal grounds for annulment is an openness to children; however, that doesn’t mean that a marriage that produced children is restricted from getting an annulment due to other legal grounds. It is a common misconception that an annulment makes children illegitimate in church law. That is false; it does not! Of course, a Catholic annulment is a separate process from a civil divorce, but the Church will ask if the civil obligations are being fulfilled.