Yes, it is proper etiquette for parents to respond to wedding invitations without their children if the invitation is addressed only to the parents' names. When the invitation is addressed specifically to the parents, it indicates that the invitation is extended only to them and not to their children.
In such cases, it is essential for parents to respect the couple's wishes and not assume that their children are included in the invitation. It's not appropriate to add extra guests who haven't been specifically invited, as it may cause logistical issues for the couple and create an awkward situation.
If the invitation is addressed to the entire family (e.g., "The Smith Family" or "Mr. and Mrs. Smith and Family"), then it is appropriate for the parents and their children to attend the wedding.
If the parents wish to bring their children, and the children's names are not mentioned on the invitation, they should reach out to the couple or the designated RSVP contact to inquire about the possibility of including their children in the guest list. However, they should be prepared to accept the couple's decision gracefully if they are unable to accommodate the request due to space or budget constraints.