Okay, I'll have an attempt at this one. Mine aren't stepkids, they're mine and dh's, aged 9, 5 and 7 months. Dh has a taste for holidays involving lots of visits to archaeological sites, so strategies are essential.
First off, is your stepsons' behaviour normal? Yes, left to their own devices kids are prone to being competitive, demanding and argumentative. This is likely to be worse on holiday when their normal routine, with its rules and expectations has been suspended. I think they also suffer from the buildup to a holiday, expecting it to be somehow amazingly fantastic, and are then obscurely disappointed and resentful when it doesn't live up to their expectations.
Is this kind of thing inevitable? No, not necessarily, but the potential for it is always there, and you need to anticipate problems rather than reacting to them. It helps to plan a holiday like the Normandy Landings if you want to minimise trouble.
I make a point of outlining to the children very clearly what's going to happen, eg. 'We're going to do one activity for you and one for me and dh every day. If you spoil the day for me and dh, then we won't want to take you to the waterpark the day after' (or whatever). I prefer this to the 'naughty step' type system advocated by Supernanny, as it's a consequence of the kids' behaviour rather than a punishment as such. I also always make it clear in advance that there will be a maximum of (say) one ice cream per day, and warn that anybody who whines for it won't get one at all.
I go out of my way to explain to them how they need to behave in order to make it nice for everyone -- eg. 'Now you're both sensible children, so I'm sure you can find a way to divide up the shells so that nobody feels they haven't got enough'. Another line that works for me when one is deliberately winding the other up is: 'Why are you trying to make X angry? She's horrible when she's angry." If one is jealous of the other it can help to make that explicit, eg. "Why are you kicking her? Do you feel she's got more than you?"
It also helps to engage the children's interest. My dh will witter on endlessly about eg. the Romans throwing people to the lions when he's taking them round a site, or explain about the evil eye symbol in Turkey, and ask them to try and spot where they can see it. Sometimes we need to take a child each (harder with more than two!) to make each one feel special and appreciated.
sorry for long reply -- hope it gives you some ideas!