First, forget Trinity Site. It is located on White Sands Missile range and is only open to the public on two days each year - one day in April and one day in October. However, the October open house is cancelled, but even if it wasn't it is tomorrow so I doubt you'd get here in time anyway. So forget Trinity (Not much to see anyway - a stone monument out in the middle of nowhere and an old Ranch house (McDonald ranch). Given that, there are two options I'd recommend (having made that trek many times) depending on weather IF (and only if) the weather is forcast to be clear, then:
Option 1 (in two parts)
Out of Tucson head to Phoenix/Scottsdale on I-10
Find your way to Highway 87, which runs northeast to "Payson"
From Payson, take Highway 260 to Overgaard, then pickup 277
Stay on 277 to Holbrook, where you pick up I-40 East all the way to Albuquerque.
An alternative, and equally nice but slightly longer route is to do as above, but when you hit Payson, stay on 87 to Winslow.
Be sure to stand on the corner in Winslow and count how many girls in flat-bed Fords drive by.
Then take I-40 as before to Albuquerque.
If you do take the Winslow route, you can backtrack (west) on I-40 to Meteor City (about 10-12 miles), then take a10 mile trip south from I-40 to see the Arizona Meteor crater. Either way, whether you come out at Holbrook or Winslow, you can head heast and visit the Petrified Forrest just off I-40 (about 20-30 jiles east of Holbrook)
Option 2 (If weather not looking good for trek through the mountains:
Simply take I-10 to Las Cruces, NM then head north on I-25 to Albuquerque. Not very scenic but much safer if the weather is dicey.