The premise is a young girl's entire family claim to be in service to 龍神 as fortune tellers. They own the Hoju Jewel which allows them to have clairvoyant powers and they use their station to connect the dragon world to the human world. Their eccentric way of going about explaining this to her embarrasses her so this is just a sentence relaying to the reader what she's been taught. She doesn't seem to believe in any of it.
その龍が神様だ、なんていうのもウソくさいし、うちみたいな田舎の占い屋が、人間界の代表であることもウソくさい。
My translation:
"That dragon is a god - this is what I'd call a sham, as is some rural fortuneteller being the god's representative for the human realm."
I'm not too sure about the なんていう + のも. I want to keep the main idea intact. I'm learning how to translate and localize text. A breakdown of this sentence would be extremely helpful.