From this end of PA you're looking at 32 hours (according to Google Maps) of pedal-to-the-metal driving in order to cover the approximately 2100 miles. That does not include rest stops, food stops, gas stops or the inevitable traffic tie-ups due to road construction or accidents. I'm going to presume you have a real narrow window in which to get out to Yellowstone, see the major attractions and get back home, in which case I can understand your motivation. JMHO here - you may be better served in the long run by inserting a day off the road somewhere in the trek out to YNP, especially if you have young'n's along. In any event, good luck & safe travels.
On edit: East Entrance is fine. Nice drive.
