I don't have any rules. 
But there are unspoken baselines which as a family we respect. So we don't raise our voices to each other, no physical violence, no bad language, no backchatting, no leaving a mess for somebody else to deal with, no climbing on furniture etc. But they're never enforced as rules just the way we taught the dc to treat us/the house/each other.
Being careful of the language you use might make a difference. So instead of 'do you want a clean nappy?', try 'right, nappy time, can dt1 get the wipes, dt2 get the nappy and then who can get back here fastest. GO!' It might be a palaver but what you actually do is you make it clear that x is happening but couch it in terms where they're active, involved participants. Similarly when getting dressed, do you want this top or this top, not 'do you want to get dressed'. Putting on shoes, pretend to put the wrong shoes on the wrong child, ask 'do these shoes go on your ears or on your feet', pretend to put them on their ears. It just makes parenting an enjoyable, interactive and fun experience but you're making it clear that certain things happen at certain times and it's not optional. Options come within that.
I find that children respond quite well to knowing what's happening and what is about to happen. Try putting yourself into their minds. Say they're on a swing and happy as anything, no concept of time, feel like they're flying, suddenly you stop them and it's 'home time now'. Huh? What? Eh? You could have a chocolate mountain and Mr Tumble himself atop it at home, but at that moment in time, you can't expect a toddler to justify the end of the swing time to themselves in any terms and they react only to the sudden change. So instead, five minutes to home time, you start framing it in terms which do make sense. So, dd/ds, it's nearly time to say goodbye to the park but we have time for two more things and then back in the puschair. Slide or roundabout? Good, now time for one more thing and then we're going to race to the pushchair. Okay, last go on the slide and then who can pick a daisy/stick/leaf up on the way to the pushchair and then we'll talk about the daisy/stick/leaf on the way home. Constant management of expectations. It does work and couple with praise it's v effective. So 'brilliant last go on the slide, you went sooooooo fast, I bet you're going to find a great stick, maybe like stick man himself, oh look how quickly you're climbing into your pushchair, tell me about your stick' etc. Of course you sound like a prize nob to everybody else but it just might mean you have happy children not banshees as you've managed the situation.
In terms of staying by you when out then that's up to you. If it's a busy place, then you have to enforce it in whatever way suits but you can also work on teaching them proper road sense, hand holding, sensible walking and do it by involving, talking, making it fun (silly walks, counting, spotting things etc) but always reinforcing how you should do it and praising them when they do.