(My answer is more generally about the back-to-the-Moon, manned program of which this is the latest iteration)
Timeline:
This post-Shuttle, job-for-the-boys, program was started a long time ago and predates Trump and Pence by a large margin.
In fact, 2004 (Bush):
President Bush proposed on Wednesday to develop a new spacecraft to carry Americans back to the moon as early as 2015, and to establish a long-term base there as an eventual springboard to Mars and beyond.
Not that Obama minded overmuch since he did little to put it out of its misery:
Space policy of the Barack Obama administration
The space policy of the Barack Obama administration was announced by U.S. President Barack Obama on April 15, 2010, at a major space policy speech at Kennedy Space Center.1 He committed to increasing NASA funding by $6 billion over five years and completing the design of a new heavy-lift launch vehicle by 2015 and to begin construction thereafter. He also predicted a U.S.-crewed orbital Mars mission by the mid-2030s, preceded by the Asteroid Redirect Mission by 2025. In response to concerns over job losses, Obama promised a $40 million effort to help Space Coast workers affected by the cancellation of the Space Shuttle program and Constellation program.
CNBC
In 2012, shortly after SLS was announced, NASA officials estimated that each mission would cost about $500 million — with the rocket targeting a 2017 debut. Today, the cost has ballooned eightfold, according to the NASA auditor.
Lobbying:
If you look at the history of NASA, big funded programs have large, large, groups of lobbyists ready to keep them alive. Having literally crashed and burned, the Shuttle needed a replacement to keep Boeing and co happy.
I read The Last of the Great Observatories: Spitzer and the Era of Faster, Better, Cheaper at NASA and it was very clear on the lobbying powers of the big guys.
They spend almost 20 years scrounging crumbs out of the budget to launch Spitzer. One year they had, IIRC, a $36M windfall earmarked for them, only to see it re-allocated, "by emergency", to the Shuttle.
To paraphrase from memory:
We tried to stand up for our budget and learned that scientific researchers and academics are totally outgunned by the lobbying capacity of big established manned programs.
Nothing all that specific to Trump and this program, under various guises, precedes Trump.
requoting the quote:
Elon Musk started amassing billions of dollars and investing in space companies. So it's a little bit unique right now because I think it will still be hard (as Boeing has found) to justify these investments to shareholders
IIRCThis is disingenuous to say the least: IIRC the amount of money spent so far on SLS represents a good chunk of SpaceX total spending to date. Besides, SLS isn't paid for by Boeing shareholders, but by US taxpayers under cost-plus structure