One tip about Old Faithful geyser, stand up wind, if you are down wind all you will see is the steam. We grew up in MT and have been to the park many times. We made the mistake of being down wind one time, was very disappointing. And as Bedlam said, if you can, go through Glacier National Park either on the way out or the way back, granted it may be out of you way, but even just driving through on the Going to the Sun Highway is worthwhile. And I think 9 days it is very doable. Neither park should take more than 3 days to see. Just do not be in a hurry and stop often.
One final note, bears are very populated in both areas so be wise and keep track of your surroundings. Bears will normally run away, but get between a sow and her cubs or accidentally corner a bear and you will have a fight on your hands.