The 'RHOA' star filed her counterclaim in court, obtained by TMZ, and she makes no bones about who their 4 children should live with going forward. Kim is asking a judge to grant her primary physical custody of the kids -- but says legal custody should be shared between Kroy and herself.

Kim doesn't get into details about why she deserves to have her children with her full-time ... the only thing she points out in her docs is that she's "a loving, fit and proper parent." She does say Kroy should be granted "liberal visitation" with the kiddos.

Kim also says she's dependent on Kroy for support and maintenance -- which is why she's asking the judge to grant her temporary and permanent alimony, on top of child support.

Keep in mind, this flies in the face of what Kroy asked for in his most recent divorce filing ... where he asked for sole physical AND legal custody -- plus child support, alimony, etc.

In terms of their shared property and assets ... Kim's asking the court to equitably divvy that all up. She also points out they have their Georgia mansion together. As we previously reported, they just listed it on the market for a cool $6 million.