Dolly Parton's nephew Bryan Seaver -- who is locked in a bitter legal battle with the company managing her estate -- is sticking up for his sister Rebecca Seaver after she was fired from the late singer's museum.

Bryan wrote on Facebook ... "I am very proud of my sister Rebecca Seaver and her endeavors building Dolly’s archive and museum, and my cousin Danielle Parton is my closest family and my buddy. We are nearest in age and have always been pals."

He added ... "I have always and will forever sing her praises and support her as she goes about her journey and career. Both of these women are dynamos in their fields and there is no feud between us. I love them both with all my heart."

Sources told us last week ... the team overseeing Dolly's estate terminated Rebecca from her managerial role at Dolly's archive and museum operations ... along with her entire staff.

As you know ... Bryan -- who formerly ran Dolly's security -- was fired over alleged texts he sent that are at the center of his legal battle with the people running her estate.

The folks overseeing her estate claim they contained threats against Dolly's businesses ... while he claims he'd never threaten anyone physically, just their reputations.