President-elect Donald J. Trump’s support for Pete Hegseth, who he announced as his nominee for defense secretary shortly after Election Day, is wobbling after a crush of controversy over a rape allegation and a 2018 email from Mr. Hegseth’s mother accusing him of a pattern of abuse toward women. How Mr. Hegseth fares through a series of tests on Wednesday will be critical for his chances. He is set to continue his meetings with key senators, including Joni Ernst of Iowa, a combat veteran who has spoken about being sexually assaulted herself, and his mother is expected to sit for...