A sweeping Trump administration plan to prop up ailing coal and nuclear plants has one big problem: The president’s own appointees could stand in his way.

The members of Federal Energy Regulatory Commission, most of whom were appointed by President Donald Trump, already thwarted one effort to bail out uneconomic power plants, killing a 2017 directive by Energy Secretary Rick Perry that sought to keep struggling facilities in business.

Now, Trump has directed Perry to take “immediate...