Completely skipping over any mention of his relationship Sif or the exact details of the emotional turmoil that drove him out of Asgard to Jotunheim in the first place, Loki answered, “stupidity. That was honestly what it was. I was angry over the raw deal I thought Thor was getting -which we eventually sorted out,” that was hopefully going to end any questions she had there. He didn't want to claw that wound open.
“I ended up in Jotunheim, got drunk in one of the villages and I mean a level of drunk that should have rendered me dead... and it seemed like a great idea at the time.” Loki shrugged. He left out the revenge part. All the anger and vengeance and hurt that went into every single coupling with his new wife. It would raise more questions about the how and why.. which would lead back to Sif. Which he wasn't ready to talk about. If he could avoid it.
“Angrboda was smart, clever and... had a temper. She liked to throw things, and yell, and hit. Sig,” Loki gave her a very serious look, “I will never physically harm a woman if I can at all avoid it, but it was getting really difficult to deal with her. I hadn't been back to Asgard at all in a long time. I cut my losses, divorce was done and instead of leaving them behind... I brought my children with me. I didn't trust her to not take her anger out on them or to not manipulate them... or worse.”
He sighed, deeply. “In hindsight... maybe I should have left them... look what happened.”