With you and your wife having driver's license for different states question is complex because it would appear one of you would need to change your driver's license to the state in which you reside in.

Since your current car is registered in New York it would appear that you live there. If this is correct than typically you would need to turn in your Maryland license to get a NYS one because according to state laws you must apply for a NY driver's license within 30 days of becoming a resident of NYS. Their definition of a resident is a person who lives in a domicile within NY for 90 days or more. So if you are NY residents the state requires you to register the car in NY and have NYS automobile liability insurance coverage on it.

If instead you are Maryland residents, which MD defines as a person whose fixed, permanent and principle home for legal purposes is located in the state of Maryland, the Motor Vehicle Administration requires proof of insurance in the form of a Maryland Insurance Certification (FR-19) which can only be issued by an insurance company licensed to do business in MD.

So according to this information from the NYS DMV (nysdmv.com) and MD MVA (Marylandmva.com) it does not appear that you can register the car in one state and insure it in another. You can get a free car insurance quote for either New York or Maryland here.