I'd say set up cams throughout the house or even a dash cam for the car. May be expensive, but at least you'd have proof

Before you jump to cameras, hold a family meeting. Everyone needs to be there- all the children, your spouse, and you. Number One: Make a chart for chores, and divide them equally among EVERYONE in the household. Everyone has to clean their own room, the rest of the chores rotate at a regular interval so no one gets stuck with the worst chores all the time. Doing chores gets them points, and they get to decide what reward they are working toward. You and the spouse decide the cost. I suggest making it take at least a month to earn them. NOT doing chores loses them points, unless it is because they didn't have time. Also, chores includes cooking dinner and (if they take lunches to school) prepping lunch for tomorrow. This way, you don't have to cook all the time, they learn how to cook for when they are older, and they learn how hard it is to cook. Number Two: Set up a list of rules. The kids should get input, but the rules need to be fair. Decide what punishment applies to what rule. Whatever you decide, the punishment needs to not only be fair but MUST be applied consistently and equally. Make a poster sized print out of the rules with the punishment for breaking a rule being beside it print it out or make copies, put one in each common room. Number Three: Make a schedule- yes, scheduled- for both the month and what an average day will be like. Put things like dinner time and homework time on there, and give each kid a block of time to talk to you and your husband by them self, or to have some time alone with you two. Put some sort of family activity, or at least an activity with you and the kids, at least every other week. Every week would be better. It doesn't have to be anything fancy, it could just be a board game night, s'mores night, reading from a book aloud to the others, or watching a movie. It also won't hurt to schedule an activity between ONE child and one parent each week, and rotate until you get back to the child you started with; the kid that's turn it is should pick the parent if possible. Number Four: This is actually the first thing you should do, so my mistake. Speak to all the kids one by one and ask them why they feel how they do, and if they can give you past instances where they felt like that. And keep in mind that, as a step parent, if they knew their other mom, they're going to be resentful about her being "replaced" for a while. That said, if their behavior about it gets any more out of control, they- and you- may benefit from counseling. The children to help them deal with the emotional drain, and you to have a way to relieve built up pressure. This isn't really a numbered piece of advice, but yelling tends to encourage the child to escalate their behavior because it means they have bothered you successfully. Keeping your voice firm (and you can still sound angry, too) but at conversation volume makes them more likely to listen because not only is it not the kind of response they want, but the fact they can have to focus on what you are saying can make it more likely to stick. Good luck with parenting, may your family thrive.