R.,
Here is the reason step parents should not "discipline," at least not for awhile. Parents care for and love a child from the time of its birth. The discipline a parent hands out comes in small doses within a context of great love, so that the child does not misunderstand at all that the parents' love is great and the discipline is just circumstancial.
By contrast, the child does not have a long history of love from the step parent. Discipline will be felt as criticism and negative feedback, without a context of love in which the criticism and feedback is received. And of course, when a new adult moves into the family situation, a child worries about change - will the new adult will like them, will it change how their parent treats them, will their comfy family suddenly become uncomfortable. A new marriage is great for you, but may be full of fear for a kid.
Parents can understand all this intellectually, but children can't. The most important goal is to help your daughter realize she remains loved and wanted, and that the new fiance does not represent a threat to that. Because discipline can be seen as criticism and dislike and undermine this goal, step-parenting books all recommend leaving the discipline to the parent until the relationship between child and step-parent deepens. Although it's difficult to put a time-frame on this, many books recommend up to two years - YES THAT'S A LONG TIME but trust-building takes a long time - while the new step- parent works conscientiously to demonstrate acceptance, so a bond of mutual appreciation and hopefully real love can develop.
In the meantime, if you agree with your fiance on the necessary changes, you don't have to wait to start making them. Remember, though, too much change at once is not a good thing. Perhaps you and your fiance can concoct a list of the things you want to change and work on one or two for a few months, and then add another one - always making YOU be the one who sets the boundaries and offers the reminders and reprimands. This may be too slow for your fiance's sense of decorum - he clearly has a different set of ideas about parenting and is uncomfortable with what he sees - but keep in mind that you do not want to force many new behaviors at once. Change is difficult, no matter your age, and the new marriage is already a very big change. Hopefully your fiance does not have a "control issue" and can learn to let go enough to make changes in a healthy time frame.
Here's what I think about different rules at each parent's house. Don't worry about it. Just as kids adjust to different teacher's expectations, they will adjust to different expectations at different households. You will no doubt hear some "daddy doesn't make me do that," or "you didn't make me do this before HE was here," for awhile. You know, both of those statements are TRUE, so don't reprimand her for saying them. Ask your fiance not to personalize this or be defensive when he hears it, and use the opportunity to tell her why you've changed the routine...maybe earlier bedtime because kids who get enough sleep are smarter at school. Or maybe table manners because she needs to know them to be a good guest at her friends' homes. In other words, you implement rules for good reasons and you may as well say why! If there's no reason then ask yourself if the rule is really necessary...
One final word. I am on my second set of kids. These kids are not mine. I hated what I saw when I walked in here - they ate McDonald's every night and lunch AND dinner on weekends, and their breakfast was a sweet roll. Our son ate no protein, fruits or veggies AT ALL, had terrible mood issues and was doing terribly in school. One of our daughters' diets was nearly as bad. I apologize to anyone reading this who thinks this is an ok way to feed kids, but I'm a health nut. There also was no bedtime. At 4, 6 and 9 they were falling asleep wherever they dropped, at maybe 11 p.m. This was the routine at both mom's and dad's. Because these things seemed like health and well-being issues, it was VERY HARD for me to keep my mouth shut - it NEVER got easier. But it turned out that Dad WANTED to change, but without support felt it was impossible. We picked issues we felt were the most important and began working on them slowly. We made their bedtime half an hour earlier each week until it got to the compromise it is today (8:30 is what we shoot for, but it doesn't always happen). We introduced "no-thank-you bites" and made a fun game out of "trying new things." We did not force foods beyond the no-thank-you bite until we knew they liked something. Dad had to make all these new rules and enforce them. My job was to build a loving relationship with the kids and coach Dad in the background. Believe it or not, neither of those jobs was easy. Being a rule-maker makes you feel mean. Biting your tongue makes you feel helpless. We fought about both aspects sometimes, but we stayed the course as much as we could.
You know what, the funniest thing happened! I actually DO love the kids now, and they know it. Our family has gradually turned into a more normal family, and I can occasionally reprimand them - from a place of love. I still let dad handle the big reprimands or the two of us do it as a united front. My point is, TRUST ME, all of you will be happier in the end if you take it slowly, no matter how hard it is for your fiance to watch behavior he hates. I sometimes had to leave the room (once I even left the house) so I didn't have to watch. But it was the best course of action for the kids.
By the way, if your fiance cannot slow down and see his role as "building a loving relationship with your daughter" and "supporting your parenting" rather than dictating behavior, you absolutely MUST get family counseling. Otherwise your wonderful new relationship will deteriorate. I've seen it happen with too many others...
GOOD LUCK. This is not an easy problem.