Are you my sister?????????
My sister is doing just this. This friday she is getting married (but with dress, rings, photos etc) with just the immediate family. It was only going to be me and the best man as witnesses but they decided to include immediate family. Then in 3 weeks they are having a 'party' at home which will be their reception for extended family and friends to celebrate. No one knows about the wedding on friday except those attending and they'll send out the reception invites this week so everyone gets them just after they've already done the formalities.
Totally normal and totally the cheaper way to go