Can anybody offer any advice or information to help us at these crossing points?
A little bribery gets you very far at the Ukrainian border....but only with the Ukranians, you try to bribe a Polish border guard and you're going to jail.
But, and I've driven in Ukraine, the best thing you could do would be leave your car in Poland take a busto Lviv. Ukraine is dangerous, worse roads and drivers than Poland.
Lviv is OK, it's pretty but nobody speaks English, it's not exactly friendly and it's far to travel by bus....tbh I wouldn't bother if I wasn't flying there