The sentence is from my textbook, where I'm asked to pick the correct or more suitable choice from inside ［ ］:
最近［ 車の / 車を持つ ］代わりに、カーシェアリングを利用する人が多い。
According to the textbook, the correct (or more suitable) choice is 車を持つ.
As far as I know, both choices seem fine to me as they follow the required grammar construction for nouns and verbs along with 代わりに.
最近車の代わりに、カーシェアリングを利用する人が多い。Recently, people make use of car-sharing instead of a car.
最近車を持つ代わりに、カーシェアリングを利用する人が多い。Recently, people make use of car-sharing instead of a having a car.
1) Are both choices right or only the second one is possible?
2) When you join two elements A and B by means of 代わりに, is it mandatory that A and B are the same part of speech?
I suspect that's why the second sentence is the right one, because both elements are verbs (持つ and 利用する) as opposed to noun and verb (車 and 利用する). But it's just my guess.