The fact that your DP doesn't have kids of his own doesn't mean that he's unqualified. My SO didn't have parenting experience before we got together, but he's been a lifesaver, and for quite a while my son (who is 8, stubborn and wants to be the boss) listened a lot better to SO than to me. SO didn't get involved to much with the details of what the kids are and are not allowed to do, but he did instill in them the message of "Everything you have, you have because of your mom. She works hard to take care of you and so you have to treat her with respect. She knows what's best for you." That ONE thing has made a TON of difference. When the kids don't follow my rules, he isn't interested in doing extra fun things with them.
I find I have a lot less conflict with my 8 year old when he knows the plan... even if it isn't anything super exciting. His first question after school is usually "What's the plan for tonight?" and I tell him what I'm making for dinner and that we are going to watch a show (the latest thing is old MacGyver episodes?! SO watched it when he was a kid & thought DS would love it....ummm, yup!) or play a game. Sometimes when he's more difficult, it means I have to let him try something I don't think he's old enough for yet... it has been an extra privilege or an extra responsibility... he just needs to feel more grown up (I don't know why he thinks acting up is the way to accomplish it... I just wait for a good behaviour moment to suggest whatever I've decided he can do. Eg: one night we let him stay up late and taught him how to play Monopoly, which he'd been asking about, after his sister was in bed)
For something like cleaning their rooms, I'd pick my moment... maybe let them know on Friday at dinner that first thing in the morning you'll be reminding them to clean their rooms. They don't go anywhere until their rooms are clean. We often have something planned for the afternoon (picnic at the beach, bowling, swimming) If one of them doesn't follow through on cleaning their room, one parent stays home with them and the other parent takes the other kid out. Each of them has missed out on the plan once, and once only. If it's something like getting ready for bed, they do it after dinner but before we get into an activity... they have to accomplish the thing they don't care about before they get to do the thing they want. It sounds like a big negotiation tactic, and it was a big deal sometimes at first... but it's just how it is now... they know I mean it when I ask them to do something, so they just do it. It's probably important to say: I don't expect perfection in anything, just that they put in a reasonable effort. If DD picks up 80% of her mess, I can fine tune it for her, and if DS decides he's sleeping in a t-shirt, I don't argue that he should wear PJ's, etc.
Have a talk with DP, and make sure he knows what the bigger picture is on the values you'd like to instill in the kids. Once that's done, the details are easier to manage. It might be a good idea to set a routine to follow, especially at first. Make sure you have some fun family time every week, or you'll end up feeling like all you ever do is nag them (and so will they!) My kids really like playing Uno and Sorry at the moment, for a while it was a PS3 game (Little Big Planet... it's a 4 person game that requires cooperation)
My SO is a school bus driver and I do before/after school care, so we get the benefit of some one on one time most weekdays. I think that's key... find a way to spend some time with your DP frequently, with no kids around.
This is getting pretty disjointed, I'm sorry!