The former couple, who separated earlier this year after six years of marriage and have three-year-old twins, Monroe and Moroccan, are trying to reach an amicable settlement before filing for divorce, but are said to be "arguing over property and custody of the twins."
A source told PEOPLE.com: "I think they're trying to work all these details out on property and the kids before it gets filed. They communicate because of the kids."
Their split has been especially difficult for the 44-year-old beauty, who was criticised for showing up too late to perform 'All I Want For Christmas Is You' at the Rockefeller Centre Christmas tree taping on Tuesday (02.12.14) because she was on the phone with her divorce lawyer "for close to five hours straight."
But the insider added: "She's trying to keep it together. She's focused on caring for her children and her upcoming five sold-out Christmas engagements in New York."
Mariah - who has yet to comment on her split from Nick - was disappointed that the lengthy call with her lawyer forced her fans to wait in the rain on Tuesday and her performance had to be rescheduled for the following day.
The source said: "She would never want to upset her fans."
'America's Got Talent' host Nick, 34, who confirmed in June that they'd been living apart for a few months, previously vowed to put their children first and was spotted visiting them at his estranged wife's New York City home for Thanksgiving last week.