Should you be allowed to register even though this is your second wedding? Definitely! This IS your first wedding to each other.
Most family and friends will want to give you a wedding shower to celebrate in your happiness.
Being registered will make it easier for your guests to select the right gift for you. However, there are a few people who believe that a second wedding should be simple and discreet. Don't let this bother you. This is a time of happiness and you should be allowed to have the kind of wedding you want.