Setting basic ground rules and ensuring those are abided by is NOT about 'choosing' the OP over his children !!
It sounds as if OP and her DP have already had discussions about behaviour/rules in their home, yet he then goes back on his word once confronted with the reality .... and yes, that's very possibly down to 'guilt', and/or not wanting to 'spoil' limited contact time, and/or a fear that the kids will vote with their feet if told off, but nonetheless, it doesn't alter the fact it must be terribly frustrating for OP to have had what she considers to be a fair and amicable conversation which her DP then all but ignores. In other words, he pays her lip service, tells her what she wants to hear, but has no intention of sticking to his word. Which is disrespectful IMO.
Furthermore, it's clear his approach - apart from anything else - is making a rod for his own back, yet he then takes it out on her because he doesn't like the extra work he's caused himself, which is ridiculously unfair. Maybe he thinks they should both be running about after these kids - or worse, maybe he thinks that as she's 'the woman', the OP should be doing it all instead!
Sorry Hole but (IMO) your response to OP was far too idealistic. I really don't think it's about her seeing the stepkids in a more positive light .... it's about her DP stepping up and parenting responsibly - for everyone's benefit, including the children. 'Accepting' that they are going to be lazy and ignore house rules - which is probably stuff that's been mentioned several times before - while their father picks up the slack and runs around after them is crazy .... what sort of message does that give them, and when will they ever learn to do stuff for themselves, or respect the household generally, and everyone who lives in it ?
This isn't about OP's perception of children - as is so often the case it's a DP issue. A dad who isn't parenting, who's taking the easy option (except he doesn't like it as he gets more work and is then unfairly snarky with OP). He could go a long way to making himself happier, his partner happier and raising two more thoughtful and well balanced kids if he simply attempted to implement house rules.
I doubt the OP has said anything 'derogatory' to him about them - I doubt very much she's called them names for example. But, in her own home, she is quite entitled to expect minimum standards of behaviour and respect - and this is borne out by her disclosure that when the children aren't there he too feels what is asked of them is reasonable. Having a moan when this doesn't happen is quite understandable - and it's very wrong she should feel she must walk on eggshells because he's so touchy about the whole business. Either he agrees with the house rules they've previously discussed, or he doesn't. If he doesn't, he should explain why that is and get on with the resultant skivvying without bloody moaning as the answer is in his hands.
But that of course would be the cowardly solution and his kids are likely to grow up spoilt and selfish if he does everything for them. Perhaps OP, in one of his more lucid moments, when the children aren't there, he needs that pointing out to him - does he really want to raise children like that ?