I think it is quite reasonable to not want your step-son with you during spring break. I also think your husband is being passive-aggressive which feels much like bullying to me. I say stick to your decision.
I suggest you're lacking the ability to follow thru. For example, he didn't put his dishes in the dish washer. Sounds like he didn't have a consequence. In order to get children to obey you have to be consistent in giving consequences. I suggest that you read one of the Love and Logic books by Foster Cline and -------. I think they have info on their web site too.
I suggest that it will help if you do some reading and then planning on how you're going to parent. It would be best if you got your husband to work on this with you. Take a parenting class. Many hospitals have them for a nominal fee. Others are also available in the community. I suggest googling parenting classes and your city name.
I suggest that the first thing you need to do is stop trying to please everybody. You parent the way you think is best. The others aren't parenting so find a way to shut out their comments. I include your husband in the group that isn't helping.
Back to Spring break. If your husband doesn't find anyone that his son can stay with I suggest that you walk out the door with your little one and leave him at home. Will you husband think that's appropriate? Or will he then find someone who will take him?
Twelve is usually OK to stay at home alone but I wouldn't leave a problem child at home alone. Tell you husband your plan ahead of time so that he does have an opportunity to prevent it. But if he doesn't then do it. Follow through!
I would be feeling similar to the way you feel. I had a difficult foster daughter. I got back into counseling and the two of us went to a counselor. It helped a lot. Even if your husband won't go, you make an appointment with a counselor who specializes in preteen and teen issues.
You must find help now before your step-son gets any older. Life can be a nightmare with an out of control teen.
Another idea is to tell your husband that you won't parent at all. Experts do recommend that the birth parent do the disciplining. There are some good books on getting along with step-children. Then you back off. Ask your husband to make a list of the rules he thinks are important and the consequences for breaking the rules. Tell him that you'll leave enforcing those rules up to him.
I was also a step-mother with a passive aggressive husband. He had no rules. Boy was 6 and wasn't required to bathe, brush teeth, change clothes. There were no rules. His father thought I was too hard on him. His father and I did go for counseling and with the counselor's help made a list of rules and consequences. His father still didn't enforce rules and his son rebelled against my enforcing them. I worked on the marriage which included working on getting along with the son for several years. We are now divorced. My ex's inability to step up and be a parent was our primary difficulty.
Do not let this situation continue. Find a way to make changes. The only one you can change is yourself. Others will react to your way of treating them and possibly make changes in themselves. I suggest that with firm and consistent parenting your step-son will be OK. That does mean that your husband has to be on board.
I also believe that you need professional help to make these changes. I urge you to get some counseling. You've tried, by yourself, long enough. You sound like you're at your wit's end and cannot continue in this way. So you be the catalyst that starts a change.
I agree with much of what JessicaWessica says. I'm suggesting that you need a break so that you can come back to the situation better rested. I didn't mention boundaries and I think boundaries are an issue with you. I had to learn about boundaries when I was a foster mother. The concept is complicated. Many of us don't learn how to make boundaries as children.
You are stating a boundary when you say you want your step-son to stay somewhere else for spring break. I think it's a reasonable boundary as well as a consequence for disobeying and arguing with you.
For me what comes thru very clearly in your post is that you don't have some specific rules and there are no or few consequences. You're fighting with your husband which make your effort towards teaching rules ineffective. When he said no, he was being disrespectful. His father didn't intervene which left you feeling helpless. Get some counseling so that you can deal with the situation in a reasonable way. Couples counseling is the best but if he won't go, you go to learn how to deal with a passive aggressive husband.