10x05 "The One Where Rachel's Sister Babysits"

Rachel's sister Amy (Christina Applegate) shows up at Ross's looking for Rachel and Rachel quickly learns she plans to marry her ex-boyfriend's father. Rachel takes her in, much to Joey's chagrin, and tries to help her get her life together. Amy offers to baby-sit Emma, who she calls Ella, but messes up by getting Emma's ears pierced. Rachel is incredibly upset but eventually her and Amy come to an understanding when Rachel finds out her other sister, Jill, is now fat. Mike attempts to propose to Phoebe on the big screen but Phoebe tells him how lame that is when another couple gets engaged that way. Phoebe tries to fix it by proposing to him on the big screen but Mike gets laughed at. Mike finally proposes at a restaurant and Phoebe accepts. Monica and Chandler ask Rachel to write a letter of recommendation for them to their adoption agency but Joey feels left out. They ask Joey but he tries to write the letter using big words, only for Joey to use a thesaurus to a ridiculous degree (to the point that he refers to himself as a baby kangaroo). He finally re-drafts the letter but gives the handwritten letter to the agency before Monica and Chandler can approve it. The agency thinks a child has written the letter and love it.
Note: Originally aired as a 43-minute episode.