I think the whole "do I do the washing up or not?!" angst as if that's a normal issue for people with decent boundaries to worry about... Really, if you are in someone else's house, isn't it normal to ask "is there anything I can do to help?" not just taking it upon yourself to do the washing up and treating them like a child? If someone has a messy house, politeness would be not to draw attention to it yourself, but to ask generally what you can do to be helpful.
Sadly, housework, running the home and looking after DCs does normally fall to woman in most families, so if as MIL you breeze in and act like it's your job, then of course it's going to come across as stepping on your DIL's toes - and if you don't have a DIL, you shouldn't be doing that for your adult DS anyway.
Treat your adult DC as adults, not children.
Treat their homes as their homes, (and respect it as you would any other person of your aquaintance) not an extention of your own home.
Remember that your DGC are someone else's children, not yours - they are closely related to you, but not your responsibility/job. You defer on all child raising decisions to the primary carer, who in most families is the mother. Don't go behind her back to try to prove her wrong and 'win'.
Basically, don't be a dick. You might get away with dickish behaviour with your own child, but your DIL (or even SIL) is not going to stand for it as.