There are already ways to enforce those -- for example, Democrats and US labor unions used the USMCA negotiations to enact a "facility specific rapid response mechanism" that lets the US essentially strong-arm Mexico and Mexican companies into improving collective bargaining rights within the context of the trade deal; section 307 products (created by forced labor) have been illegal since 1930 (and enforced more strictly over the past decade, given concerns about Chinese slave labor); carbon import taxes addressing environmental regulations have been proposed in Congress, but haven't been implemented yet. The government also has existing authorities under anti-dumping and countervailing duty (ADD/CVD) legislation, so long as those duties comply with American obligations under international treaties (Trump's tariffs exist outside the ADD/CVD framework, and place the US in noncompliance relative to our WTO obligations).
Trump's tariffs don't really serve any specific policy goals other than "trade is bad and everyone should buy more from us than we buy from them," which is self-evidently absurd; why are we punishing Madagascar because we buy their vanilla and they're too poor to have extensive need of our services-based economy? Beggar-thy-neighbor trade policies inevitably beggar us as well, as we're likely to find out quite soon.