What an awesome idea - way to make the best of the situation! I’m jealous (I usually spend a few weeks a year in the US and no idea when that will happen again).
The ideal is obviously both bikes, but gravel bikes are really ‘do it all’ bikes. You can still take it on easier trails and have a ton of fun, and much nicer on road/dirt roads. If you were going to Colorado/Utah I’d probably say MTB, but even then as pointed out, renting would be a really good option. I have a CX bike and MTB - the CX is the work horse doing 'cross, gravel, road, bimbling, commuting, quick runs to town, etc. Much more versatile.