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The first thing you do need to understand is that you certainly can't do this trip in 2 days, and even 3 days (each way) would not be recommended. Your trip is nearly 2000 miles and you really are looking at 3.5 days minimum to do this safely - and even that is being on the road for 10-12 hours each of the first 3 days, with really no time for any extra stops at parks and natural sites. If you see bad weather, you would need even more time.

Camping will also be a bit of a challenge too. March can be a very fickle month for weather, and even in areas where it may be comfortable during the day, it still often gets quite cold at night. At the very least, you'd need winter camping gear. You should also expect that some campgrounds will still be closed for the season.

The drive itself shouldn't be too difficult. Interstates are designed to be driven year round by long haul truckers, meaning that grades and curves are limited as much as possible. Gas miles may change a bit in the mountains, but you're talking about a difference of just a few miles per gallon.

The most straightforward route would be I-15 to I-70 to I-76 to I-80 to I-35 to I-90. The logical stopping points on a 3.5 day trip would be around Richfield/Salina, UT, Sterling CO, and Des Moines IA.