Kim Zolciak Picks Kids Up From School in Midst of Divorce War with Kroy Biermann

Kim Zolciak isn't letting her ongoing divorce war with Kroy Biermann stop her from taking care of the couple's 4 kiddos ... still going full mommy mode to keep things as normal as possible ... despite the fact her estranged husband is gunning to take the kids.

Check out the pics, obtained by TMZ, showing Zolciak driving her Range Rover Wednesday to pick up her son, Kane, from school. Our sources say this is a regular occurrence, but something Kim wants to continue to do in order to keep the kids comfortable and calm.

Kroy stated in his divorce petition he wants sole custody of their four kids -- he wants them to live with him, though he didn't specify where. Our Kim sources say despite what Kroy insinuates in the docs, both Kim and Kroy are still living under the same roof with their children.

TMZ broke the story, both Kim and Kroy filed separate divorce petitions, a clear indication things are getting very nasty behind the scenes.

Kroy is asking for both sole legal and physical custody of the kids, without any mention of visitation for Kim. He's also asking she vacate their family home, the same one that went into foreclosure earlier this year.

For her part, Kim's asking for sole physical and joint legal custody of the kids, with visitation for Kroy.

We were the first to report the estranged couple is in serious financial trouble, owing more than $1 million to the IRS ... in his divorce docs, Kroy requested Kim maintain all financial records -- including expense reports as well as income and tax records.