Even if you do that, NY will require you to change the cars regie back to NY after 60 days. Now you can probably get away with not doing it, but.. you could also get jammed up a bit.

Not if you dont have a VA drivers licence.

Look into that.  You may be requred to get a VA license.  I don't know their laws, but most states allow a max of 60 days, and some a lot less, before requiring a change.  

A lot depends on where you pay taxes and are registered to vote.  The voter registration is an act of residency.  If you pay NY tax, VA can't really touch you if you work part time there.  However, that in itself may be another angle favorable to you.  If their taxes and other circumstances are better in VA - you'd have to research this, I don't know - establish residence there.  Only some prick cop or idiot judge would have you switch license/registration/insurance back and forth because you alternate 60 day+ stays.  Generally nothing happens, and a reasonable explanation of alternating work locations (stressing the word "temporary") is fine.  BTW, most NY cops are quite reasonable if you are reasonable yourself (probably the best in the region).