Generally, kids respond positively when their is some sort of structure and regularity to their lives or consistency, or validation to their feelings/concerns just thoughts and/or praised for just trying their best etc.
One thing, that is really helpful, (it may sound old fashioned but it does help)... is to have a regular, perhaps weekly or twice a month "family meeting." It doesn't have to be all "serious." But, do not use it to scold or blame any child or use it as a forum to just lecture "at" the kids.
Making it a nice family time... where you can all talk about what is on your minds... what as parents that Dad/Mom has to do, what is coming up, what are expectations for the week, how the kids can HELP and THEIR ROLE in it all... to designate chores or help around the house. To organize the family. If Dad for example needs to say fix something in the house or change the light-bulbs.. then he can have one of the kids "help him and therefore learn something fun/responsible at the same time. The KEY THING being... to make the family "meeting" something that is bonding for all... fun... productive AND that will make EVERYONE feel like a TEAM. Or you can make "lists" for what each child and even Mom and Dad is responsible for... and how that helps with the family.
Defining what "family" IS. That it is about everyone having each other's back and caring... and communicating openly, WITHOUT fear of being criticized or fought with or judged.
Another example is: instead of asking a child "What did you do today?", or "Did you behave today?"... ask the child INSTEAD "How did you help the family today...?" Do that consistently... and over time, it will change the construct of what "they" did versus what they did as a PART of something... maybe making them feel more proud of what they are doing... at home, IN the family.
I do that with my kids... it makes them think twice... and it makes them feel REAL proud that they did something for the family not just for themselves. BUT... no matter what the child does "for the family"... no matter how small or how big... you MUST be proud of them, even if they did not do it "perfectly." If you criticize them in this endeavor and life lesson, they will NOT want to do anything for the family, Mom, Dad, anymore. It will defeat them, and dishearten them, crushing their morale.
Kids also... get used to the world revolving around them.. but by this age, they also need to learn that they are a PART of the Family. They are not just living by themselves... they are a PART of something bigger. And.. if they want to be a part of the family, the HAVE TO be a part of it. Not just off doing whatever thing they want, without regard for their Parents.
Next, when you talk with them... have you just point blank asked them "why" they have such a bad attitude toward their Mom/Dad? Do they like their Step-Dad? Does he "like" them? Is the problem with him and them... or with you too? Was it always that way... or just when they had a Step-Dad? Sometimes kids "resent" step-parents... or that their Mom re-married... have you investigated that as well?
Maybe they are having trouble coping... with the changes in their family...
Or, do they still see their biological Dad? Is there any problems there?
Perhaps, they just feel that nothing matters... either. Sometimes, and as a kid myself... whenever I felt that NOTHING I did mattered, then it just made me more of a "brat." Or if I felt a parent was not really understanding me... or was just expecting me to be what THEY wanted me to be... or if I was just not heard. So.... in essence, a child gets apathetic. Then sassy and full of attitude. It is a sort of "rebellion" against the parents, when kids get like this. They do have a reason... even if it is deep down inside of them... and it is not pleasant.
The main thing, is to get to the ROOT of the problem....otherwise, punishments and grounding will not make a difference. And, they will just feel like nothing matters. They will get, or are already... just indifferent to it. Indifference being a feeling when someone just gives up, or does not care, anymore.
So, find out why... they are acting this way. If, you feel it is something beyond just "normal" developmental changes.
Still, a kid with attitude problems... is not tolerable nor acceptable.
Just some thoughts,
All the best,
Susan