What is the difference between qi3 and qi3 lai2?
Verb + Directional Complement

The direction verb immediately following the verb and indicating the direction of the action, is called the direction complement.

If the object is a thing, it can be placed as:


  他**带**了一份合同**回来** (Tā dài le yí fèn hétóng huílái)


or


  他**带回**一份合同**来** (Tā dài huí yí fèn hétóng lái)


[Source: 当代中文 (Dāngdài Zhōngwén) Book 2, 2nd Edition, 2006]

You can Google directional complement to find more information as well as quizzes, so you can learn more about it and test yourself.

P.S. if you are teaching beginners, with pinyin only, this sentence construct is beyond them.

EDIT: sorry I realise I only answered via inference. To be clear, the reason why we don't say it your second way: because grammar, that's why. An arbitrary set of rules that all (read: most) people agree upon :)