Am I being unreasonable with this kid?

I'm currently in a relationship with a woman that has two kids (we will be together for 2 years soon). Neither really has their father in their life and both are out of control most of the time (I'm trying to set a good example and provide positivity in their lives). The oldest one is 14, he's smart, but he won't do anything you tell him to. His mother has taken away game consoles, internet, phone, tablet, access to the TV and whatever else she can to punish him. He will argue, yell and scream, say horrible things, throw things, punch walls, talk bad to his semi-autistic 6 year old brother instead of doing simple things like taking out the trash. It will go on for an hour even though the task could take less than 5 minutes.​I like to take all of them on adventures (I think it helps to bond and also raise their quality of life by providing positive experiences), so now I'm using those adventures as punishment for bad behavior. Last week he refused to do his chores, or he would do 1/8th of them and say he was done. I find it rude, but I understand he's being a kid. His mother was done with it all and very upset (he keeps her pretty angry 75% of the time). She told him to take a shower, it didn't have to be a long one, just get in and clean the important things.. "but I took one yesterday, I'll just take it tomorrow".. Arguing happens and he acts like he's going to hop in, but doesn't.. Just goes to his room. Me personally, I'm upset with it. It seems so trivial (to argue) and necessary to shower daily as a 14-year-old and of course he shouldn't just dismiss his mother like that. With that said, I had planned to take him and a friend to go camping at a Ren fest as a surprise (we all really like that sort of thing and go when we can). With the way he's acting, I don't want to drop a few $100 on him, so I tell her to cancel the adventure. He finds out because his friend asked him what he did to get it canceled and gets upset and then tells me that he will show me that he cares and he's sorry by doing all of his chores. He does almost nothing at all. Sunday we left him at home and went without him. He was upset, but I felt it was a good punishment.​Over that past few weeks, we've been telling him this type of thing will happen and that we've got some pretty good things lined up for him and his brother. He's been pretty rude, name calling, horrible to the 6 year old and then throwing things around just like the 6 year old throwing a tantrum, for a month now. Last night, his mother told him to take a shower again and again "I'll take one tomorrow because I don't smell" (I point out that he doesn't smell because he had a shower the day before).. He yells and screams, calls everyone names etc. So I tell him, go knock out the shower or you aren't going to this comicon (as he's been aware this is coming up).. It didn't phase him one bit. He said he had done all of his chores, so I have to take him and that I'm being unreasonable.. I point out, that the chores are apart of living in that home and that I don't live there. I am free to provide fun or not, it's up to me. (he likes to point out his rights to us and tell us what we are legally allowed to do).. Once I tell him he has lost the chance to go, he tells me I'm being unreasonable because it's "just the one thing" that he did.. (it was really a ton of things that lead to this). He's as big as his mother and get's violent, he just doesn't hit anyone. Hitting him isn't an option for me unless he gets combative with others.​I see it all together as bad behavior and I do not want to reward anyone for yelling, screaming, name calling, throwing things and defiance. With that said, I'm new to this, I was dropped into this situation and I may not be the best with it. I'd like to see if the seasoned professionals of this sub think I am actually being unreasonable or going overboard? via /r/Parenting http://bit.ly/2Gx0iJY