Planning a spring trip - PA to UT/MT and back again

Hey everybody,

I'm in the beginning stages of planning a trip in the spring to head out west. I have family in Utah and Montana and have never been any further west than Dallas, so I really want to get out there and see the landscape.
For those who have taken trips like this before, I wanted to get some collective advice, opinions, suggestions, tips, and whatever else might be helpful. I will include a list below to outline the trip so far.

• The trip would have a timeline of about nine days (I would take a full week off work plus an additional day or two at the end/beginning of the week prior/after)
• I would leave Pittsburgh and visit family in Utah, then potentially in Montana, then back to Pittsburgh
  
• The target is for the third week in April, most likely 4/16 through 4/25
• I hate to fly... like seriously, hate it
  
• I love to drive but trying to comprehend exactly how much time I will actually spend behind the wheel
• I looked into taking a train, but it isn't cheap and might even take longer than driving
• I looked into flying out one-way and renting a car for exploring and the drive back to PA, but it will be insanely expensive
  
• I love to camp and "rough it," having done plenty of camping in the past out of my Taco. Would prefer to camp out in a state park as opposed to a hotel, in other words
• I would want to take the Taco but it has 225k miles and many original parts (clutch, suspension, etc.).

I'm open to any constructive advice, ideas, etc. Thanks!