Sources with direct knowledge tell TMZ ... Kristin was "surprised" that Jay filed first -- she didn't know he was doing it. There's one thing in his divorce petition that set her off ... his claim that he was the "at-home parent" who was the "primary caretaker" of their kids.

We're told Kristin was shocked and claims Jay was not telling the truth ... she says she has been the primary caregiver.

So, that set up the battle. Jay is asking for joint custody. Kristin, in her response, asked for primary physical custody with Jay getting visitation.

Tennessee is a "fault state" -- meaning someone asking for a divorce must show fault on the part of the other spouse, and that's why she claimed Jay is guilty of "marital misconduct." It's actually boilerplate language in the state. The language is included in a divorce petition and counterclaim because Kristin and Jay can't end the marriage without some showing of misconduct. As for what the misconduct is ... that's for the lawyers to handle.

There have been a bunch of rumors Kristin wanted out because Jay had an affair. We know there was a buzz about this on their reality show and the "other woman" was allegedly Kelly Henderson, who denied there was any relationship between her and Jay. It doesn't matter, because that has nothing to do with the divorce.

We contacted Kristin's lawyer, Rose Palermo, who had no comment other than to refer us to Kristin's post over the weekend saying the divorce was amicable.