That's right unless @miuratohko 's fiancé has a brother coz she mentioned he is the second child (out of how many children? We are not told...) and has an elder sis but did not mention if he has any other siblings such as a younger brother. If he has a brother, then it would be "eldest son" instead of "only son".. I would assume that "youngest daughter" would be correct as miuratohko mentioned that there is the youngest bro after her (which I take to mean that is the youngest sibling she has regardless whether she has any elder brothers and that she has no younger sister)...
The guy is not the youngest son since he is the second child and the first child is a gal. He is either the only son if he doesn't have any brother but if he has any brother, he will be the eldest son..
The printer will print whatever that's given to them. They may be able to advise you but it may not be accurate. Just read my initial reply to your post; it should be right depending on your fiance's situation - my dad's done freelancing copyrighting including wedding cards for quite a long time before this so I've also picked up a thing or two from him...