Dear D.,
From what you have described, it sounds like your step-son is indeed having difficulty in certain developmental and behavioral tasks. I'm wondering, however, is it because he can't do the tasks or he won't do them? Do you know if he has the skills necessary to do the things you ask of him, or does he seem sad, lonely, or troubled about something, and maybe his behavior is trying to tell you what he can't say in words?
Please do whatever is humanly possible to put personal feelings aside and develop some sort of co-parenting relationship with the mother. Yes, I know this is hard, but you don't have to be best friends or hang out together. Whenever there is tension between parents (e.g., your husband and the child's mother), children sense it and feel it. It affects them. Like it or not, you and your husband do share parenting responsibilities with this woman, and you all must act in the best interest of this little boy. He is going to need all the adults in his life to be on the same page and be his champion for whatever it is he needs to correct these issues in order to prevent future problems. (By the way, I am a step-parent, too, and one of the best things that ever happened is when the children's mother and I started talking and being on the same page with regard to the children's behavior).
How about school? What do his teachers say? Surely, they must notice some similar things. How are his grades? Talk to the teacher and find out. If there are issues here, these would be independent observations that would make it more difficult for your husband to deny problems. It may be that he could be tested within the school system and recommendations for addtional services could be made. Start now before the problems get bigger.
Talk to you husband and give him specific examples (like those in your post and whatever his teacher reveals) about where your son is experiencing difficulties. Tell him how much you love this child and want the best for him. Tell him you fear if these things don't get corrected now that he will have trouble later in school as well as just getting along in life, in general. When a child experiences behavior problems that are not addressed early, the problems spread to other areas: academic, social, emotional, etc. This puts the child at risk for a multitude of lifetime problems.
I know you have a lot on your plate with a baby, toddler, grade-schooler, a pre-teen, and a husband in addition to your job, but this little boy really needs attention! Some things you can do right now: turn off the t.v ---take the remote away if you have to and limit t.v. watching to a minimal amount (yes, he will balk, whine, and cry---that's okay. Turn it off, anyway). Get down on the floor with him and do puzzles, play games, read books. Continue to strengthen the loving relationship you have with him, and resentment will not be a problem. Enlist dad to go outside with him and ride bikes, go to the park, toss a ball around. Children are more likely to do activities if the people they love do the activities with them. If there are other stable and healthy adults in the family (grandparents, aunts, uncles), get them to help, too. He needs to be away from the t.v and involved in healthy human interactions that can help him develop the skills he needs or the avenue to express what might be bothering him.
When trying to get him to do something, you first have to know whether he can do the task you're requesting him to do. For example, an 8 year-old should be able to tie shoes and dress self, but CAN he do these things? Do you know if anyone has ever shown him? If not, he needs to learn. You can do this by modeling, step by step, and with lots and lots of patience and repetition. Look for progress, not perfection, and praise all attempts toward the required task. For simple meal preparation, engage him by asking him to do little things like making his own PBJ sandwich, washing the fruits/veggies, etc. Again, if he hasn't been shown, show him how to do it first, and praise all attempts toward task completion. Little by little, he should get it. If not, there is something going on, and he may need some occupational or other therapy.
You seem to be a loving, kind, and concerned parent. Trust your instinct and do whatever is necessary to get this dear child whatever help he needs now. Do not let this go on and risk his problems multiplying. It may not be easy, but don't give up! Whether or not you know it, he is counting on you!
All the best to you and your entire family,
J.