If that's the case, put your foot down more when they're with you. If it's true, it means they don't feel like you have any power or control in your house. My SD acts BETTER when I'm around because she knows I don't play around and I stick to the rules. 

My DH claims similar things occasionally and also claims that certain things she does are only to me. That's definitely not true but he tries to pretend it to make himself feel better. He thinks hes an exception to how she treats people and one of the few people that care about and understand her. Both of us know that crap but he isn't ready to fully accept that shes turning out to be a miniature of her mom so he will go back to story sometimes.

Well then, he has a problem, doesn't he? His kids are rude to you, so what is he going to do about it?

Well, duh!  I'll bet they also speak conversational French, have an instinctual grasp of higher mathematics, and whistle while they do housework without being asked.  But as soon as you appear they are so traumatized that they regress into inexplicably rude people.  How strange.....  It is almost like he should be parenting them or something!

Of course they are. They’re probably competing for his attention and jealous, and if they make trouble they think they’ll drive you off. It might not even be a conscious thing. Also, he probably notices their bad behaviour more when there’s someone to witness it. 

Soooooo... is this when HE is around, too? If so, why is he allowing his children to be rude arseholes to an adult? Because he's a crap parent is the ONLY reason.

If they only misbehave when you are around and he is not, he has just given you THE excuse to never be alone with his young jerks.

OMG I get this sometimes too and it drives me crazy because he just ignores stuff when I'm not around so it 'doesn't make  a scene'!!!! UGH you have my sympathy.

Web cams. That way you can sit down with him for a side by side comparison of their behavior when you are there and when you are not there. My guess is that he is oblivious to the issues that you see.

It's easy to lie when you are not there to observe what is really happening.

Who cares how they behave when you are not there. That doesn't change the fact that they misbehave when you are. 

Classic not my kid syndrome. 

Next time he pulls that line out of his hat just say 'that's great DH, so you should have no problems' and go do something fun on your own. Get that drink with your girlfriends. Or go shop for shoes. I would do this every time daddy not my kids comes out to play ;) 

I guarantee you they are not that well behaved when you are not around. That’s just his imagination and wishful thinking running wild. But let’s just say they were. He still needs to address that.

Sometimes kids act up because they want attention - or don't want you getting it from DH when they're around. Children are egocentric, thinking only of their own needs. DH needs to do a better job of explaining that in a family such as yours everyone matters and everyone needs attention, including you. Also, parents often defend their children regardless of it's warranted or not. Some parents will not admit that their little "Johnny" or "Susy" is capable of being less than perfect. It's unfortunate that you have to be subjected to this unfortunate situation.

I’d not go to his house when kids are there. Id stay in my house and let SO come take me on dates. I’d not visit his house when kids are there until he teaches them how to behave. If they behave like this with the guest (you), imagine how terribly they’d behave if yiu two move in or marry?