By James Oliphant and Gram Slattery ATKINSON, New Hampshire (Reuters) -Donald Trump and his Republican opponents kicked off a week of campaigning in New Hampshire on Tuesday ahead of the state’s nominating contest, with the ex-president’s competitors battling to slow his march to the party’s White House nomination. A day after Iowans gave him an overwhelming victory in the first vote of the 2024 presidential contest, Trump, who faces multiple criminal and civil cases, appeared in a New York court to defend himself against charges that he defamed writer E. Jean Carroll after she accused him of …