If you must meet them, remain a DJ. I just had to meet my GF's (she's 9 years my junior) mother...
Needless to say, she tested me just as any woman would. One example, when she showed up there were flowers (a dozen roses in a vase) on the table. My gf was in another room changing. I had met the woman not five minutes before and she starts up with...
Mom: "These are pretty"
V: "They sure are, GF 'got them for me'."
Mom: "Huh?"
*akward pause on her end*
Mom: "Do you ever buy her flowers?"
V: "No."
Mom: "WHAT!"
V: "I don't care to, and more importantly, I don't need to: I have more important things to do with my money."
Mom: *authortitatively* "You really should buy flowers for a woman, they really enjoy it."
V: *looks at her as in 'how dare you tell me how to act', gets up from the table and goes into another room to do 'stuff' without saying a word, but not before burning a hole in the back of her head with my gaze*
My GF comes to me later, after the evening was over and her mother left, and confesses to me: "My mom thinks you're mad at her. She thinks you hate her."
V: "Oh yeah? Why's that?"
GF: "She was saying something about the flowers."
V: "Oh, that, well, she's got no business telling me how to act. Or for that matter, what you enjoy me doing. She's not me, and she's not you, but throughout the night she wanted to project her lifestyle/views/opinions/wishes/wants on us, as if they mattered. I think she was quite disrespectful, actually."
Needless to say, the next day, her mother was very ladylike, very respectful, and quite polite. She was seeking MY approval, not vice-versa. None of her crap was going to fly with me, and I would flat-out bust her sh¡t when she tried. She would talk to me like I was a teenager, and I would assert my manhood. She is, after all, a woman to be DJ'd like any other. I can't even tell you how many statements were met with a "you've got to be kidding" look from me.
As for the father, well, guys are guys. But, you'll likely encounter the same sh¡t tests from a feminized father as you would the mother. The response should be the same: be a man and don't take crap.
Go into it with a mindset as such: "You parents had BETTER like me, because your daughter does, and YOU are going to have to deal with that."