Did you look at the link in my earlier post ? A trip up through the Great Basin to Yellowstone. You wouldn't need to go all the way north to Glacier NP, you would just head to Yellowstone from Twin Falls, possibly including Craters of the Moon. Then heading south through the Grand Tetons to Flaming Gorge and the North rim of the Grand canyon and to Zion NP back to Vegas.
Yellowstone does not fully open until into June so you should check the nps website to see what is open and accessable and what is not. You could still see snow in May.