I'm not seeing much of a cost saving by alternating trains and cars. Everytime you rent a car, if you drive it from point a to point b and then drop if off, you will have a one-way charge. These are usually several hundred dollars (amounts vary). So, each time you do this, you will have to pay this drop-off fee. That would add up fast.

If you rent a car for the entire time, I'm seeing rates for about $2200-2800 including the one-time drop-off fee. Of course, you would need to add gas for that.

For the train, the longest pass I'm seeing is for 30 days at about $500 each. So to depend on trains would cost more than the car, I think. Well, maybe less as you wouldn't be buying gas but the savings wouldn't be all that much.

Really, the best thing you could do is play around with the different websites for car rentals and the Amtrak website and see what you can come up with. But I think your money and time would be better spent on just renting a car for the whole trip.