In Invitations^x, Apostrophes^x

I am making invitations and am not sure if I should use the apostrophe after the s or before? as follows: Come help us celebrate Madelyn Maries Duchene's or Duchenes' 1st birthday. Any help you can give would be appreciated

I am working on an invitation and would like to use proper grammar. Cortnie and Josh have different birthdays, but are celebrating on the same day. How should I write "birthdays"?

How about a last name being used to end a letter or invitation (i.e. last name of Smith). Is it The Smiths, The Smith's, or The Smiths'?