Kristi Noem and Husband Bryon Divorcing After Cross-Dressing Claims, Her Mom Says

Kristi Noem and her longtime husband Bryon are calling it quits, according to her mother ... just months after claims surfaced about him cross-dressing and wearing fake boobs.

Kristi's mom, Corinne Arnold, spoke to the Daily Mail at her home, which borders the estate where Kristi and Bryon lived and raised kids ... and she told the outlet it's been a difficult road for the pair -- but the writing has been on the wall for a while now.

You may remember ... in March, a few weeks after Kristi was removed from her position as the Department of Homeland Security head, the Daily Mail published a story in which they said Bryon snapped photos of himself wearing oversized fake boobs and chatted with adult performers in the "bimbofication" fetish scene ... focusing on their massive fake breasts.

The report claimed Bryon told people he wanted "huge, huge ridiculous boobs."

Kristi's team later released a statement which read, "Ms. Noem is devastated. The family was blindsided by this, and they ask for privacy and prayers at the time."

Bryon and Kristi married back in 1992. They share three children and four grandchildren.