Sounds like your parnter is not a good parent. Difficult to change. 

How old is skid? Once they reach a certain age...very difficult to change as well. I personally believe past 9yrs old or so, it takes major intervention to correct poor behavior. 

Sometimes the only thing you can hope to change is the way YOU feel about things. 

You can feel how you feel. No one can change that. We've all been frustrated by something in steplife. It's par for the course.

The question isn't whether we feel that way but what we're going to do to STOP feeling that way. What is the situation that is causing the problems? Are we talking a young kid who is learning how to follow rules, or who was parented for years without rules? Because those kids will need reminders of how to behave. That's especially true if the rules between houses are vastly different.

Did your partner help create the rules or are these rules that you set and expect others to agree to (like ESMOD mentioned)? Your partner not enforcing the rules likely means they don't agree with them and are right when they say they don't need reminded. They are an adult, and not doing something like that is typically a choice, not an accident.

Is it really that everyone is miserable or that you're just miserable? And if everyone is miserable, why is that? Is it because SK's behavior is truly unruly and your partner doesn't parent or have expectations been set too high for the kid based on age/situation?

If 50% of your life is miserable, then you need to make changes to your life. If this is a situation of your expectations being too high, then you'll have to figure out how to compromise or leave. It's okay to not be cut out to be a SP. If, however, this is a situation where your partner doesn't parent his child effectively and the SK behaves poorly due to that, then you can talk until you're blue in the face about it and hope for change, accept the situation for what it is, or leave because your partner can't juggle being a parent and being in a relationship.

You will never be able to enact and enforce rules on others enough so those people fall in line with what you want without becoming a toxic person. That's not to say you shouldn't have rules, just that you need to be with someone who is on the same page as you and is willing to live similarly. If they don't want to do that, you can't force it.

I talked to my therapist about this yesterday. My wife has been enforcing or not enforcing the same rule for two years, if ss doesn't get ready by a certain time he cannot use his screens. He always breaks it and she always allows it. It's also funny how my wife always raves about how quiet it is in the home when he's at school. It's like the whole mood changes when he walks in the door. He's loud, obnoxious, and always butting into conversations without even knowing what he's talking about. I totally understand you. 

Your SO needs to understand that they are raising an unlikable kid.  Kid will still love parent even if parent tells kid no.  They may occasionally say they don't but kids can be manipulative little tyrants if they think they can get away with it.  Trust me, my dad told me no more than once, he set rules in his and step mom's home and guess what?  It didn't change my love for him.  And he didn't get remarried until I graduated high school.  Best case scenario is both parents set and enforce rules.  They don't even have to be the same rules. Just back each other up.  I knew my dad would enforce his rules and mom would back him up, even if she didn't have the same rules in her house.  You respect the rules of whoever owns the home, whether it's a parent, grandparents, aunt, whoever.