I'm having an outdoor wedding, and being Catholic, it has been very hard finding a Catholic priest or deacon to officiate the ceremony. But since I'm what you would consider a "holiday church-goer," I'm not really worried about getting married by a nondenominational priest, minister, or deacon. The thing I'm worried about is making sure my children can be baptized. So can children whose parent's marriage is not recognized by the Catholic church be baptized? What is the wedding was blessed by a priest?
Yes, as baptized Catholics, your children can be baptized in the Catholic Church even if your marriage will not be recognized by the Catholic Church. If you keep looking, you may find a priest who will perform the ceremony out of doors. The priest will have to apply for a special dispensation to conduct the ceremony off church grounds.