I hear this mistake almost every day.
会話
▸ 「お父さん, 今夜車を使ってもいいかしら」
「うん, いいだろう. でも母さんにも確かめておく方がいいよ」
“Can I possibly have [take] the (family) car tonight, Dad?”
“Well, I guess so. But maybe you should also check with your mother.”
車で
▸ 車で大学へ通う go to college by car [in a car] (!in one's car は可だが ╳ by one's car は不可) / ride to college in a car (!ride … by car は避けられる) 【自分で運転して】drive to college.
▸ 車で家へ帰る途中で on the drive back to one's home.
▸ 彼を車で家[駅]まで送った I drove him home [to the station]. (!home は副詞)
▸ 彼女は週末になると車で富山の両親に会いに行く She drives over to Toyama to visit her parents on weekends.
▸ 車で迎えに来てください Please come to pick me up.
▸ 彼の家へは車で20分です It's a twenty-minute drive to his home.