In German there is a "standard" order of sentence parts and this is what your teacher was trying to convey. This way you will always get grammatically correct sentences.

Notice, though, that German has a sentence structure which is a lot less strict than it is in English. Therefore, apart from the "neutral" structure your teacher taught you it is indeed possible to move parts around for emphasis. Beware, though: not everything is possible and this is an advanced stylistic device! If you use it you better know what you are doing.

Having said this, emphasis is usually achieved by moving a certain part to either the end or up front. These variations of your sentence are also possible and grammatically correct, i have marked bold the part i put emphasis on:

> Meine Oma fuhr gestern das Mietauto viel zu schnell in die Kurve.

This is the "neutral" form, nothing emphasized particularly.

> **Gestern** fuhr meine Oma das Mietauto viel zu schnell in die Kurve.  

Perhaps the other days she didn*t?

> **Viel zu schnell in die Kurve** fuhr meine Oma gestern das Mietauto.  

This sounds IMHO more natural in *Perfekt*, statt "fuhr" "hat .. gefahren".

> **Das Mietauto** fuhr meine Oma gestern viel zu schnell in die Kurve.

i.e unlike her own car, which she uses to treat differently?

In spoken language one would mark the emphasis by also altering the tone in which the emphasized part is spoken.