Taylor Frankie Paul Rejected 'Substantially' More Time With Two Older Kids

Taylor Frankie Paul rejected a temporary custody agreement which would have afforded her substantially more supervised time with two of her kids ... TMZ has learned.

Sources familiar with the proposed custody agreement Taylor turned down tell TMZ ... her ex, Tate Paul, proposed giving Taylor approximately 35% parenting time with her 8-year-old daughter, Indy, and a 6-year-old son, Ocean, while the juvenile court case remains pending.

We're told the proposed schedule -- which was offered to Taylor on Monday -- included visits every other weekend from Friday through Monday, as well as a midweek overnight visit.

Our sources say the proposed deal was made in an effort to align Taylor's parenting schedule with the time she already has with her 2-year-old son Ever ... allowing all three siblings to spend time together. Ever's father is Taylor's other ex, Dakota Mortensen.

Sources tell us all parenting time would be supervised by Taylor's family ... preferably her sister, Aspen, though her mother, Lian, and father, Jeremy, would serve as backup options. These visits would take place at Lian and Jeremy's home ... and Taylor would not be able to take the children to her residence without supervision.

We're told she declined the proposal ... even though it offers "substantially more time with Indy and Ocean."

Our sources also claim Taylor has declined virtual and professionally supervised visits with Indy and Ocean ... and hasn't exercised all her available parent time with Ever.

However, sources close to Taylor says Tate and Dakota each offered her separate custody agreements that would have given her 40% custody time ... which she rejected.

Our Taylor sources say is gearing up for a lengthy custody battle with her exes, who she believes are in cahoots.

We're told she didn't exercise all her time with her children because she was following medical advice to switch medications, and even that was used against her when her exes insinuated she had a drug addiction problem.

Earlier this month, Utah's Division of Child and Family Services filed a petition asking a family court to find that her three children are abused ... and to order protective supervision services.