Can you give me the proper etiquette for second marriage weddings regarding the ceremony, gifts, etc.?

A second wedding should not appear to be duplicating or competing with the first. If this is a multiple wedding for both bride and groom, the ceremony is traditionally small and informal. However, it is really up to you. Weddings can range from very small to grand, white dress weddings with kids as bridesmaids. It may help children to be a part of the wedding, rather than have them feel excluded. Check with your church or clergy regarding second marriages, as some are reluctant to marry divorced people. If you feel uncomfortable with guests bringing gifts, perhaps you can word the invitations specifying your preferences (your presence not presents desired, donations preferred to a charity, or food shelf gifts, etc.) Else, just go for it and let your guests decide what gifts they find appropriate.