I had another thought for how to handle the "her scolding your kids/you not being allowed to correct her kids" problem.
Have your stance be, "do not scold or correct or chastize the other woman's children." And you follow it too.
But that doesn't mean you can't TALK to her kids, or ASK them things, right?
So you deal w/ her kids jumping on the sofa by saying, "Hey, Joey, c'mere a minute." And then you put your arm around his shoulders, and you say, in a very friendly voice, "Jumping on the sofa is fun, right? The only thing is, it can break. You probably don't think you're very heavy, but you are actually a pretty big kid. And I have a cousin who snapped the wooden beam in grandma's sofa by jumping on it. And there are springs inside the sofa that can get bent, and once they're bent, that's it.
"Fixing a sofa is pretty expensive--I'd have to just throw it out. And a sofa costs about six times as much as an XBox. So I'm going to ask you, please, not to jump on our sofa. Would you do that for me?"
Bingo--you never scolded her child! You simply explained the problem and asked him a favor. What could be wrong with that? And that is what you say to her if she complains.
If her kids come yelling and shrieking in your house, you whisper to them (want a kid's attention, esp. when the kid is being loud? whisper!! The more quietly you talk, the more attentively they'll listen. Try it), "Joey, c'mere a minute."
And then you say to them, in that warm, friendly tone, "I have a problem when there's
too much a lot of noise inside--it makes me stressed out. And it gives me a headache. Can I ask you not to yell and scream in the house? I'd really appreciate it. So would my headache." And then when they say "ok," you smile warmly and say, "Thanks, Joey. You're a really considerate kid, y'know that?"
Did you notice I crossed out "too much"? I did it on purpose. Get rid of the idea that there's some sort of objective "kids don't yell inside" / "nobody jumps on the sofa" concept, and treat every one of these situations as "something I'm asking this child-who-isn't-mine to do."
The child will probably listen better, and your friend can't argue. If she does, you just be AMAZED! "I'm so surprised--Joey was just helping me with a request of mine! It was very nice of him to listen to my reasons, and he was such a considerate kid in agreeing to it."
And of course, if Joey forgets, you as his friend simply remind him--"Hey, Joey, remember you told me you wouldn't jump on the sofa?"
Sharing, do the same thing. Pull Joey aside for you (as his friend who happens to have a little more experience than he does) to explain that sometimes kids don't want to share specific toys, and that you think it's respectful to your daughter for her to be able to reserve some of the toys as "not for sharing," and would he help you, and help your daughter, by choosing something else to play with?"
Slow it down, take it out of the "discipline and rules" mode and into the "sharing, teaching, and asking for help and cooperation" mode.
You'll both remove any excuse for HER to chastize your children, and you might model for her a better way to deal with other people's kids.
And you might even help those kids by explaining how the world works, and establishing for them that there is a *reason* for rules.