S.J.
V.,
I want to make sure you understand up front that I'm giving you some things here to think about... playing devil's advocate. I'm not condemning your plans. Only you can decide what is right for you. My husband and I talked about having a smaller wedding, but so many people wanted to share the day with us, we expanded.
Unfortunately, if you go by the Emily Post (Miss Manners), anyone can attend a wedding ceremony. They just can't invite themselves to the reception that might follow. If you do decide to send an announcement, you don't mail them until the morning after the ceremony and the wording is different than an invitation, but don't get your feelings hurt if they choose not to attend an after party or bring gifts. A wedding announcement doesn't require a gift.
Now....
You want to have a small private ceremony, they feel like you are leaving them out of one of the most important days of your life. You say you're inviting 2 friends a piece. I know I'd have my feelings hurt if my family member invited some friends to their wedding but left me out. You might want to write out a list of pros and cons for allowing your family members to attend. Then, think about how you would feel if you were the one not invited. Since you're planning a reception after the fact, why not allow those who want to share to be there with you. There is also the thought that being invited to a reception without being invited to the wedding, means that you don't care enough about them to share the day with them, you just want the gifts. Now you know why there are so few small weddings!
Another option would be to quietly get married at the "rehearsal" and then, "renew your vows" later in the day for the others to share in. It could all be in the same day, therefore not confusing anyone with anniversary dates or long explanations.
Good luck in making your decision! There have been a lot of people who have been where you are right now and there are no "right" answers. Do what you think is best.
Congratulations!!