Joe and Tina Simpson File for Divorce While Rumors Circulate
updated 10/24/2012 AT 04:00 PM EDT
•originally published 10/24/2012 AT 12:25 PM EDT
Their statement to PEOPLE Wednesday came the same day that buzz built around a story in the National Enquirer reporting that Joe had come out to his family.
"It is an amicable split and there is no third party involved," says the rep. "Any other related allegations are completely false. The family appreciates your respect for their privacy at this time."
Tina, 52, filed for divorce in Texas last month, and cited "discord or conflict of personalities" as grounds in the court papers obtained by PEOPLE. She and 54-year-old Joe – a manager and former minister who is often referred to as "Papa Joe" – were married in Texas in 1978 and are also parents to Ashlee Simpson. They have two grandchildren between their daughters.
In Joe's response to Tina's divorce petition, he requests Tina not get anything in the split.
None of the Simpsons has spoken out further about the split – or the rumors.