I think the talk of expanding coal production in particular was mostly talk aimed at a segment of the electorate (although I haven't followed Trump closely enough to realize the extent to which he realizes this).
The demise of Appalachian coal was mostly due to the rise of both natural gas and Wyoming coal, as well as exhaustion of readily available resources. Though Appalachian coal is higher grade, it requires expensive and dangerous mining practices such as room and pillar mining, mountaintop removal, or more traditional practices in increasingly small and geometrically complicated seams. The coal from Wyoming is basically at the surface and can be strip mined at scale very cheaply, with lots of automation.
Unconventional oil and gas production is also at odds with coal production. As you've said, oil can't get that much cheaper, and gas is pretty similar, and has more substitution with coal. Many of the restrictions on unconventional production (i.e. fracking regulations) are done at the state level, and given the concern over recent seismicity in associated with injection of post-fracking wastewater, the states probably won't budge that much. If as pro-oil a state agency as the Oklahoma Corporation Commission (the main regulatory agency in OK) is tamping down on production processes, there is very little a Trump administration can do to shift the needle.
Similarly, we (he) won't be able to simply deregulate and re-invigorate mining. Too much of the demand is based in China, and a trade war there will simply depress prices further. Additionally, many of the resources are in states that are not overly favorable to Trump, and the state EPAs have a lot of sway, especially in a more 'states rights' environment. Rare Earths, for example, are mostly found in the US near Las Vegas but across the state line in Mountain Pass, California. And NV isn't as red as it used to be either.
Lithium production could increase, but I think the problems there are there just aren't a lot of good sources, not environmental regulations. Lithium is tied up with salts or brine (salty water) from hypersaline lakes that dried up and concentrated metals that were already especially abundant due to particular geology. Lithium mining is often just pumping salty water out of aquifers or dredging it from lakeshores. It's not like copper or gold mining/processing that involves nasties like mercury and arsenic.
Trump's policies will probably mostly involve somewhat symbolic, macroeconomically insignificant, and locally damaging exploitation of currently off-limits areas like ANWR, offshore CA and the east coast, and possibly many of the new national monuments in the West that may have uranium or other metals.
Eliminating the tax incentives for renewables is also likely, but may not yield as much permanent damage as environmental degradation; some companies may lose market share or capitalization, some may bust, but this won't turn the tide.