Lack of discipline is that same as no discipline. 500 warnings is not discipline. If you go out and kill someone you don't get a warning about it... If you rob a bank you don't get a warning... if you beat your kids you don't get a warning.
Welcome little A, this is life, get over it.
If you don't see yourself out of there soon, I would for the sake of your sanity, your chinnie, and the new baby talk to the family. If you have a video recorder record him being naughty, then find videos on youtube that are similar and ask the parents what they think of that child... when/if they say they're a little monster say well it looks a lot like this huh and show them the video their child.
When our kids were really bad, we'd video them and show it back to them later so they could see exactly how they looked when they acted out.
Depending on the parents you might be able to just explain that their child is not ready for a new baby to be born and you're worried about the baby, kids get really jealous of new babies when they're been the only child. Sit down with them and explain what you'd like to see, and suggest a plan, and ask that you all agree on a plan so you're all working together, instead of undermining each other, and when he acts out prevent any undermining by saying " you're mom and dad and I have already talked about this and this is going to happen" It will remind them what they agreed to, and before enforcing the new rules, give A. one sit down with the parents and you to go over the rules. People say talking to children doesn't work, but I'll tell you that if you warn them... they see seem to remember some of it, and what they don't remember they recall after proper discipline.
Bethany, I understand you're in a tough spot. All kids here get treated the same, if it's my kids, my nieces, or my friends kids. If you're having problems with back talking I'd definitely let your husband know you're at a loss sometimes and don't feel like you have the "right" to discipline them if he's not around.
Even my niece who's parents supposedly live penny by penny is spoiled rotten. She wasn't happy with the present she got from us for Christmas and made it known. I got a game for her and her sister and each of them a very soft micro fleece blanket. They already have a ton of toys... My kids noted that they got less presents this year in private to me later, not directly to the ones who didn't get them anything this year. So many kids have no proper manners, especially old fashioned thank you cards and such... just something gone. Very sad.