The 'Just a Girl' singer and her 52-year-old ex-husband - who have sons Kingston, 12, Zuma, 10, and four-year-old Apollo together - are in negotiations about the arrangement they currently have, as the Bush rocker is keen to increase his access to the boys now his tour commitments are over but the 'Voice' coach wants things to stay as they are.
A source told E! News: ''They don't agree on custody and the time the kids are spending with each of them.
''Gwen believes that she provides a consistent living environment and that the kids should be with her the majority of the time.
''They are older now and taking their school work and activities seriously. She thinks Gavin still very much lives a rock star lifestyle and it's in the kids' best interest to be with her.''
And the 48-year-old singer is said to be concerned about the 'Swallowed' singer's ''priorities''.
The source added: ''She wants to raise the kids a certain way and it's very challenging because Gavin has different priorities.''
After the couple split in 2015, the children have spent most of their time in Los Angeles with Gwen - who is now in a relationship with Blake Shelton - and Gavin previously admitted he found it a ''challenge'' having to make a new ''home'' for them away from what they were used to.
He said: ''It was weird because I had to go and make a home from scratch that could compare to the great one they already have. That was the challenge for me as a dad.''
Meanwhile, the No Doubt frontwoman previously spoke of how well her sons get along with Blake.
She gushed: ''The kids love him. We love him. Everybody loves him.''