The We Can't Stop singer previously used the social networking site to vent at her dad after finding out her mother had filed for divorce.
The day after her mum started divorce proceedings, she tweeted: "Since your texts and email obviously aren't working would you like to talk like this?"
The Achy Breaky Heart singer did not reply.
Billy Ray, 51, first filed for divorce in 2010 but he and his wife put aside their differences as they reunited a year later.
The couple have split again, with Tish citing "irreconcilable differences" in her legal papers as the reason for the end of their 19-year union.
She is seeking full physical and legal custody of the couple's only minor daughter, Noah, 13. They also have Braison, 18, together, while Billy Ray adopted Tish's children Trace, 25, and Brandi, 23, from a previous relationship.
The actor has another son called Cody, 20, from a relationship with Kristin Luckey.
- Bang! Showbiz