Ukraine border isn't closed for private cars, but it's controlled by Nazi bandits from the Ukrainian side and you can be easily robbed or even beaten and raped by them, I'm not joking there are hundreds of accidents and even videos on youtube, "official" Ukrainian goverment in Kiev just "doesn't notice" this. Most people who drive by car there cross Kerch strait by ferry from Taman peninsula, ferry crossing takes only about an hour. My friend used this ferry a month ago and said it's very well organized, convinient and pretty cheap. I myself got there by plane and rented a car in airport just because I was afraid that almost 2000 km drive will be too hard to withstand for my 5 y.o. daughter.