Yemen has returned to full-scale war after four years of relative peace, with the Iran-backed Houthi militia seizing control of parts of the country’s Red Sea coastline in recent weeks. The group is fighting Saudi-backed Yemeni government forces on several fronts, while cross-border attacks in Yemen and Saudi Arabia have intensified. The renewed conflict has opened a second front in a Middle East war that began when the United States and Israel attacked Iran in February, adding to regional uncertainty, energy-market turmoil and pressure on the global economy. Crown Prince Mohammed bin Salman, Saudi Arabia’s de facto ruler, signed a strategic defense agreement with President Trump a year ago and has repeatedly asked Mr. Trump to intervene militarily against the Houthis, who belong to the Iran-led so-called axis of resistance alongside Hezbollah in Lebanon and Hamas in Gaza. Mr. Trump initially rejected those requests, then directed the Pentagon over the weekend to prepare airstrikes before reversing course and deciding to hold off, according to Trump administration officials. The renewed fighting raises questions about how the Houthis advanced so quickly and what the escalation means for parties with a stake in the conflict.