Teddy, I can only imagine what you must be going through. A few days after I moved here, my new two year old stepson was staying with us for several days, and in my mind, I had pictured all the fun things we would do together, but unfortunately, he screamed and cried most of the time and wouldn't let me touch him because he didn't know me yet, and I just thought it would be like that forever.
I can't say being a stepmom has been a walk in the park, by any means, but I do find it very rewarding now, although he doesn't live with us full-time, which is both good and bad. Good because we get some time alone and I get some Me Time, but bad because the hard work we sort of put in every weekend to "train" him on how things work at our house feels like one step forward and two steps back. It's like he forgets the rules before he gets here again and then has to learn all over again. It is frustrating, but I do feel I have more good times with him than bad ones, and I get lots of cuddles and attention from him these days which is a great reward after putting in a lot of effort to build a relationship with him. My advice, contrary to what some other people might do, of course, is to just jump in with both feet. Go ahead and give it a shot. What I mean is, help them with homework, tell them to clean up after themselves and just try to think of them as your own kids. It takes some hard work and they may not go along with it at first, but keep at it and eventually they will see you as a real parent and start to listen to you. At least, that's what I think and what has helped me. When my stepson wanted daddy to do everything, I would have to tell him that daddy was busy and then convince him to let me give him a bath or whatever until he got used to it. I didn't let his dad do all the work because I felt uncomfortable, I just jumped in and did what I could to help. It's tough, I know. But, stand your ground, don't let them walk on you or disrespect you, and do the best you can. You will make mistakes. You might yell one day and feel bad about it later. All parents make mistakes, but hey, it's how you learn what works and what doesn't.
Some good tactics are turning chores into games. See who can do it the fastest. Give a small prize or reward (winner gets to play video games first, or play with a shared toy for a while). Don't be afraid to be silly and try to make boring things fun! They will get into it when you make funny faces and try to lighten things up. And distraction during tantrums always helps. Try to direct their attention to something else if you can.
Good luck, it's tough going, but you will slide into a routine in no time.