Right now, the GF is EXPECTING you to back down and let her kid do whatever he wants. Deep down inside of her, she has to know that isn't right. Or even if she's really dense, tell her and brother. "GF/brother, please keep nephew off the table. I'm trying to get dinner ready." So turn the tables on her and EXPECT her to behave in a decent way/get her kid to behave in a decent way. If he crawls on the table, return him to her and said (in a 'duh' type of voice) "He's CRAWLING on the table when we're trying to EAT. TAKE CARE of it."
It doesn't always work, but I've found that when kids/adults are EXPECTED to do something--even something that isn't in the norm for them--they will do that in order to not make waves or draw attention to themselves. So don't apologize for ANYTHING. What you are EXPECTING is socially acceptable behavior. There's nothing wrong with that.
If, by chance, she counters with 'but we let him crawl on the table at home', then you can respond that while it may be ok at their home, it's not ok here. Just like it wouldn't be ok in a restaurant or when having dinner with the queen. So please keep him off the table, because you're trying to get dinner ready. And if she'd like to get dinner ready while you corral nephew, that would be fine too.
And during dinner, make sure the kiddo has a place to sit, complete with a tray and some confinement, if possible (we had a traveling high chair with a tray that sat on a regular chair when our kids were little). Set it up between bro and the GF, and emphasize that it is his spot. Even Helen Keller had to learn to eat off her own plate when her new teacher came to live with her.
But again, EXPECT that the GF/bro will parent their child. Practice it; the looks, the responses, the tone. It CAN work.