Does wife have any legal right to the car that I bought while we were separated?

Yes, any property your purchased while legally married (even if separated) is community property and therefore jointly owned by you and your wife. The exception to this rule is if you executed a prenuptial or post marital agreement wherein you decided that what you buy belongs exclusively to you and what she buys is exclusively her separate property. Contact a family lawyer in your area to start the divorce process so there is no confusion about the division of assets in your marriage.