Paul Thompson, 21 and from Ballywillan Crescent in the seaside town, is accused of common assault, making a threat to kill, criminal damage, possession of a weapon and threatening to destroy property to endanger life.
He denies the charges against him, but was refused bail at Belfast High Court on Wednesday.
Presiding judge Mr Justice Gillen said domestic violence was "an absolute cancer in this society".
He added that he was "profoundly concerned" by the prosecution case that the alleged incident from which the charges arose happened in front of the couple's children - aged three and 11 weeks.
"It is absolutely appalling that this kind of behaviour should be carried on in the presence of these children, which could cause long-lasting - if not permanent - damage to them," the judge said.
Earlier, prosecution lawyer Kate McKay told the court that, just after 11pm on 27 December 2012, police were called to the Coleraine home of Thompson's partner.
They were said to have found her in a "tearful" state, with red marks on her wrists.
She claimed Thompson had assaulted her and threatened to burn the house down with her and the children still inside.
Ms McKay added that officers uncovered a Samurai sword in a bag belonging to Thompson, who was arrested, interviewed and charged.
The court heard that, during police questioning, Thompson denied making any threats or assaulting his partner, claiming that the red marks were as a result of him having to stop her slapping him.
Defence lawyer Conor Maguire said that while there had been "an incident," he submitted that Thompson denies emphatically that he made any threats against his partner or his children.
Thompson was remanded in custody and the case continues.