Hi, this comes up time and again, it is so hard because we don't know what will be an issue til we are living with it and it is hard to sort out whilst in the midst of it all.
I posted on a previous thread about sitting down with DP and have a full on meeting about house rules, consequences, praise, rewards. You need to agree the rules. I suggest at the ages of the children having a meeting with them too, so they can input, but it is vital you and partner need to be speaking with one voice, so you need to get your position sorted first.
You are not being petty, in our house the rule is we put the loo lid down, we put our shoes in the right box, we put toys away, we switch lights off, we put washing in washing basket. These are not extreme standards, this is how our home works. But it took a lot of work for me and my DP to agree these things - he was strict on some things, me on others. We had to talk it all through and agree. I suppose our saving grace was in terms of how to get kids to do things we agree - rules, sanctions, rewards and consistency. So we just had to negotiate/compromise on the actual rules. Also my DP can be a bit slack at first then too tough second time, whereas I am a teacher by trade so used to being tediously inflexible consistent, we had to practice being more similar (and I had to lighten up at times).
If you cannot do this, or if your partner refuses to even discuss any meaningful discipline etc, you may have a major problem.
It is also wrong that you can't discipline, this is where the house rules works - it is then a case of 'this is how it is' rather than you telling them off. Your partner should back you up so they know if you tell them it is exactly the same as him telling them.