There are a lot of things to consider here. First of all, since this child has been in your life and care almost since birth, the family issue is as much your duty and responsibility as it is your husband's. And, since you cannot wave a magic wand and make the bio-mom disappear, you and hubby need to find a mature way of dealing with her (whether she chooses to be mature or not!) You should decide which of you is better able to deal directly with bio-mom and, although you both need to present a solid front, that one should be the one to be the primary spokesperson. Ideally, you should all be able to handle and resolve issues in an adult manner but, given bio-mom's background, that may not be possible.
You are well aware that your stepson is operating from minimal social and relationship experience. His expectations are those of a six year old and so he relates to things on that level with no awareness of the overall demands of a child's wellbeing. That is why parents are deemed responsible for the actions of their children until they reach a certain age. And that is why you and your husband have custody of your son. it is imperative that we, as a society, provide the best guidance and nurturing of our children that we possibly can. Understandably, you are frustrated with dealing with your son's expressions of dissatisfaction over his living conditions when you sacrifice so much for him. And it is easy to let that frustration shift to anger. Just be careful you don't let that anger manifest itself against those who are not responsible - like your son. Try to recognize that the anger is merely a logical response to the frustration you feel of the situation.
Now, since your hubby's ex- was deemed an unfit parent and you (you and your husband collectively) were given responsibility for her child, it falls to you to help your son understand WHY he cannot live with his mother. This can be kind of tricky territory to navigate since you need to make him understand the courts believe he would not be properly cared for by his bio-mom but you don't want to appear the nasty, wicked stepmother dissing the mom. When you tackle this, be sure to let him know that his other mom loves him but she has some problems of her own and sometimes she may do things that are not right for her or for him. Try to find ways to relate those big, grown-up issues in a child's realm of understanding. ("If we are hungry and I fix something for me to eat but don't feed you, that wouldn't be right, would it?" or "If Daddy and I go somewhere and leave you at home all night alone, that could be scary for you. You would feel sad because we left you all alone and the police could lock us up for doing that to you." and "But we would never do anything like that because you are the most important thing in our lives." but "Sometimes, because of her problems, your other-mother might not be able to see that something is not necessarily good for you." so "The court says you cannot live with her.") This segues to my next point.
Some other things to consider:
You also have some possible legal alternatives. You don't say whether your son stays overnight with his bio-mom or if the court order allows or restricts the type of visitation she may have with your son. You also don't indicate whether the child custody order was issued prior to, or in ocnjunction with, your involvement with the family. If the court documents list you as a party to the case, that can simplify future legal actions.
If the court dox stipulate that bio-mom may have overnight visitations or there is no stipulation concerning supervised vs. unsupervised visitations, you may want to go back to court to clarify and/or modify this issue. If you feel the visits with bio-mom are too disruptive, you might want to check into restrictive b-m's access by Motion for no overnight visits or, if she has no overnight visitation, further restricting visits to supervised visitation only. This will allow her to spend time with him but will not give her control over the situation. That is, she may be able to see him at an exchange center or Safe Place (where the visits can be monitored) but she would not be allowed to take him home.
Also, does the bio-mom contribute anything toward child support? Regardless of her personal financial situation, this should be a given and she should be made, by court order, to contribute to her son's maintenance.
The toughest thing to do, as others have already mentioned, is to take your personal feelings out of the equation. Remember, in the final analysis, you want to do what is best for your son, your family, and your relationship with yoru husband.
Lastly, in the final analysis, in years to come, your son will know you always tried to do what was best for him and he will love you for it. That is your greatest reward for the heartache and emotional turmoil you feel now. And it's worth it ... HE'S worth it.
Good luck and, if you need a shoulder to cry on or a compassionate ear, drop me a line.