What is wrong with saying "de auto van mijn oom is sneller dan die van mij" ?
As per El2theK's response above, it's probably not acceptable because it doesn't mention "car" twice.
Wagen really should be added to all the sentences...
'Nonkel' is not a synonym for 'oom'? It is not accepted.
It is pretty much only used in Belgium, and since this course focusses on Dutch that is used in the whole language area nonkel is not included.