Your gut is right.

She's trying to turn you into a bf.

You are friends with benefits. Nothing more. You are not obliged to meet her family. Yes, she is trapping you.

What would I do? Either next her, try and fuck her as many times before her hamster kicks in and says 'let's go exclusive', or just say no to her.

'Come meet my dad'

'no'

I think you know the answer already

If you don't want to go, don't go. Simple as that.

Get out while you can. This part:

she started complaining about men always using her for sex despite bragging to everyone that she can have sex with no strings attached at all

screams "I actually crave attention and am not in it just for the sex as I previously claimed". Then wanting to hang out more without sex and asking you to come meet the family during her time of need.

If she really just wanted to be FWB she'd only want the D. Sounds like she wants much more than that though.

Well, I have some advice..

I think it would be similar to the other advice you'll get in this thread..

You know what you have to do, brah..

Do you like her as more than fwb? Go. No? Don't.

I would go. Why interrupt a sure thing on this plate? Go and hang out wherever. Have fun. If shit goes south with the FWB and she pulls this out hanging out as evidence that you wanted more...just mention you had a "straight forward agreement" and that any thing else was in her head. You have an agreement that this is all for fun. Unless she communicates specifically that she wants to be bf / gf, it is not YOUR problem.

...i happen to have a for lack of a better term a longterm FWB that we both know there is no healthy monogamous relationship there, hang out with each others families, and constantly have to put them in their place that nothing more than great friends who occasionally fuck when we are both single. we have been doing this for going on five years now. Open and honest communication is key. the real challenge is to figure out if you keep her around because you actually value her friendship and opinions or if you are only in it for the ass. if it is the former discuss your feelings about it with her, if it's the later then gtfo out dodge.

my advice: bail for a while and in a few months after not seeing each other, you can reach back out to see if she is down for the FWB thing again, but I wouldn't

You need to cut off all ties with this person. For both your sakes.