You didn't specify how Yellowstone would erupt. It's not a given if Yellowstone erupts, it would be a supervolcanic eruption, and if it would, there likely would be major precursors and warnings, it's not going to blow massively out of nothing in complete surprise, but good, even if i'm not right and it would be a supervolcanic eruption.
It would have major impacts for the surrounding states which are republican, they would still stay Republican. The entire US would be engulfed by the ash cloud, and it would travel around the world, but in less high concentrations. The climate would change enormously in short term, and almost everything from modern climate change would be undone for a while, perhaps entirely undone, as the cooling involved with it might return the climate after it's impact is over to pre-industrial normal levels.
It would be a major crisis, and a lot would depend on how the Trump administration would respond. If it's not serious to them, they will be punished for it. I however don't think Trump would minimalize such a volcano eruption as the direct impact itself will be major, but i'm not sure if the Trump administration would be capable enough to deal with it, and it will be easier to create opposition (others however prefer stability during crisis, and therefore go with the incumbent, but Trump isn't exactly a pillar of stability).
I honestly think the Democrats would do better in this TL than the covid TL.
It could get considerably worse than that. At a minimum, the Feb 2021 winter storm in Texas would be an annual event. In the extreme, it's 50 years of constant January and basically all US agriculture outside of Hawaii and the Gulf Coast has to be moved indoors or abandoned entirely.