In my house, it's our rules that come first, much like I teach my son that when we go visit, we need to be considerate for *that* family's rules.
For example, if kids were running around at my house, I'd likely try to step in in a positive way: "Oh, I see you are done eating. You are welcome to sit at the table and listen, I can bring you some paper and crayons or I can get out (age appropriate activity-- say, bristle blocks). We have walking feet in our house, so figure out where you want to settle down, now." If that still was being ignored, I might ask the parents "do you want to take the kids for a quick walk? We really don't have room for running around in here."
It is ideal that we expect the parent to correct the child, but I think we've all had experiences when parents were either checked out or just ignoring bad behavior. I don't, and I don't feel it's in good service to the children, either. During playdates, even when parents are present, I always review the rules and address all the kids in this way.
I'm also very matter-of-fact that general 'good behavior' guidelines need to be met. Not picky about precise manners, but I will send all the kids, one by one, to go wash their hands and use the bathroom before a meal or help direct all the children in cleaning up. I think that if we aren't shy and just treat it as "this is how we do it " instead of "Your kid needs your attention, they're being a pain", it goes over better.
If I'm a guest at someone else's house, I do have basic rights there too, and so does my child. If a kid was climbing on my chair in the way you describe, I'd simply say "Oh, I'm using this chair now. You'll need to find another place to play." If my child was preverbal and couldn't speak for himself, I'd speak for him "Oh, Kiddo was holding that. If you want to use it, ask me please, and I'll help you so you can offer him a trade." My son is older and I more or less encourage him to speak up for himself...or if the company is unpleasant, we can find something for him to do close to me (workbook, coloring). I also have no problem with saying "Oh, well, it's probably time for us to go-- looks like the kids are timing out with the boring grown up talk!" and leave it at that.
At 42, I'm sort of in the "you can like it or lump it" perspective about these sorts of things. Your precious angel has no more right than mine, or the adults, to have a pleasant time. And if their parent has some inhibition or philosophy that impedes them from expecting common courtesy from their children-- let's just say that I am not suffering from the same affliction. I'll help where I can, and be as positive about it as I can, offering choices and reasonable options, but I'm not a shrinking violet. And I don't want my son to think that it's appropriate to just get walked all over 'to be nice'. ugh. So if I've done my best, offered choices politely and pleasantly and a parent who ignored their kid chooses to take offense-- well, too bad, huh? Life's too short....
Oh, and here's an article I really liked on Mamas On Call pertinent to the subject:
http://mamasoncall.com/2012/12/my-house-my-rules/