You are correct that you should be able to select further ordinances to print off once earlier ones have been completed. You may want to look under 'My Reservations' or an individuals person page to select the ordinances you would like to do next. If you look under 'Ordinances Ready' you will only see male ordinances if you are male and female ordinances if you are female.
The article below might be useful to you in this situation.
I Cannot Print a Family Name Card
I hope his enables you to solve your problem 😊0