"They have to register their guests."
Translation:Ihre Gäste müssen sie registrieren.
Can we flip the word order and say "Sie müssen registieren ihre Gäste"? Would that be correct too?
That syntax is wrong. You might say 'Sie müssen ihre Gäste registrieren' though.
That's not completely true anyway. You've got a compound verb here, which is 'registrieren müssen'. As far as I'm aware, it's subject, verb, object or o-s-v, if you want to stress the object. For my translation it's Subject, auxiliary verb, object, verb.