Is it rude to have two weddings?

You should have the wedding you and your partner want which may look like a church ceremony and formal dinner. You shouldn't have a full reception with dancing and a cocktail hour if that is not the intimacy you're looking for, and certainly not because family guilts you into doing so on your dime.

Now per your question if two weddings is rude-- I don't think so. You really are legally married with the first, but it's up to you if the symbolic wedding counts. However, your guests may see you as already married and this is essentially a friends vacation. This is problematic as most people like to use their own PTO from work and their own money for their own vacations. What you have planned is a trip on YOUR schedule (not an ideal vacay). But, really ask yourself if you really want to plan two major events in the future. A wedding is difficult enough with personal emotions, family issues, and host duties/ expenses. Coordinating a group vacation for 12 people is an even heavier endeavor. Some couples are so tired from wedding planning, they wait months or years to plan their honeymoon, and that's only for 2 people.

My suggestions: unless you don't want your friends to meet your family, invite everyone to a dinner party reception. OR, have your private family-only wedding (no apologies), and wait for a friend to throw you a local party. Couples trip in the future.