He is actually not in control of the senate. They are republicans. Trump is an outsider. They might side with him on some issues, but they are not under his control.
I agree that the Trump 'administration' is responsible for the shutdown. In fact it was his duty to follow what the experts and advisors told him to do. These were the CDC, WHO, and Fauci (who created the virus in a lab). They all told him that it wouldn't be a big deal until it was too late for him to do anything. So he did the 2nd best thing. He shut down the economy. The dem controlled news made it worse by fear mongering a virus that we now know only kills the elderly and those with pre-existing deadly conditions and it only kills those that are vitamin D deficient.