Kelly Clarkson Wins Primary Custody of Children in Divorce, Husband Wants $436k Monthly

Kelly Clarkson just scored a big victory in her divorce case ... the judge just awarded her primary custody of their 2 children in Los Angeles.

Kelly and estranged husband Brandon Blackstock were fighting over custody of 6-year-old River and 4-year-old Remy. Brandon apparently has decided he wants to live on their ranch in Montana and wanted joint custody of the kids where they could be shuttled back and forth between L.A. -- where Kelly lives -- and Montana.

Disso Queen Laura Wasser, who reps Kelly, argued that her client felt Brandon's position would be detrimental to the kids, and the judge agreed, saying, "The court finds that the minor children are not now and have not been residents of Montana and that California is their home state."

The judge gave Kelly and Brandon joint physical and legal custody, but the upshot is that Kelly will have the kids most of the time. The judge ruled Kelly has primary custody of the kids in L.A. and Brandon gets the kids on the 1st, 3rd, and 5th weekends of each month. The 1st and 5th weekends Brandon must be in Los Angeles in order to spend time with the kids. As for the 3rd weekend of the month ... the kids would travel to Montana.

Although it's technically joint physical custody, Kelly will clearly get the kids the lion's share of the time, which is what she wanted.

The order also says neither Kelly nor Brandon can talk smack about the other to the kids. The order also says neither parent can consume booze or weed within 8 hours of driving a car with the kids inside.

The divorce is ongoing.