I'm sure this is so very hard for you. I can see how unfair it must all seem.
I was a competitive swimmer when I was younger and can still swim very well. When I went to Mexico a few years ago, I allowed my confidence to take me out in the water in a different area, but still close in, to where I saw others. Before I knew it, I was caught in the undertow. I panicked and struggled (I haven't swum much in natural bodies of water). Finally, something in my brain kicked in. I looked to the shore. I saw the life guard. He was motioning me to go to the left. I stopped stroking, stopped fighting, and I allowed myself to be carried in the direction he pointed. Soon I realized that I could feel the sand beneath me. I stood, exhausted, and walked from the water. I could have died that day. I really could have. The panic was intense. My efforts were extreme. Only when I stopped fighting and put my trust somewhere else and allowed myself to be carried, did I survive.
I really and truly hope that what I am about to write does not sound harsh or judgmental. I do not mean it that way. I think you are caught in the undertow and you have lost your ability to find your way to shore. I think people here, and the GAL, and your lawyer are trying to tell you things you don't want to hear.
As horrible and sucky as it sounds, not everyone can defend their case in court the way they want to. I have the money to fight my case, and the skills to close the gap, but I chose not to go head to head with my H even when he was being pig-headed and I would have been within my rights to let him have it and suffer the consequences of his actions. It was not worth burning everything down to get my way. From all you have said, you don't have the resources to fight the fight you want to fight. Given that, you have to fight the fight you can.
I know that I have given you advice, as have others, that you have seemingly ignored. I would suggest you go through and read your own thread from the beginning and see what people have said, consider whether you thought about it, and consider whether you acknowledged that it was heard. There is a difference between being right and being self-righteous.
I think we all want to truthfully report our stories and endeavor to do so, but there are always factors that we don't report, or that we don't give the right weight to. Often we don't consider the other guy's position, or how we look to him (to the court, or the lawyer, or the GAL).
I'm not sure I still understand your marital situation and the allocation of resources. Were you married under the law? Are you divorced? Was your wife required to pay you any support other than child support? Are you getting support through the child support office? Most states are pretty formulaic about child support now.
These things matter because you have indicated that you have serious health concerns, very limited resources, and very little family support. If you do not have a legal entitlement to support (and fairness is of course a different issue), then it would be understandable that some consideration would have to be given to the parties' respective abilities to care for the children. I have no idea if these issues are relevant in your case or what consideration the GAL gave to them. I am only hearing you describe what sounds like a very unfair situation and trying to figure from your interpretation what has happened here.
GALs go through a lot of training. This is not a big money-making field. The people that go into this kind of work generally do it because they are deeply concerned for the rights of children and making sure they have a voice. I admit to being part of the legal system so I understand that there are bad lawyers, bad judges, and bad GALs, I also understand that most lawyers are nowhere near as bad as I see continually reported on these boards, and I imagine the same is true of the judges and other court professionals.
I think the counselor, the GAL, your lawyer, and others have been trying to tell you to put away your perceptions of what is right, fair or just, and to have some faith in the system, and if your wife is as bad as you say, to trust that she will not be able to handle whatever it is that the system gives her. It sounds like she has no interest in two of the children at all, and a passing interest in the third. Is she really going to give up her life to tend to three children that are about to be tweens and teens. As the parent of two teens, I can tell you that I don't see that happening based on what you have described.
Take a step back. Evaluate your position. Look at the good and the bad. There are 3 kids, they look after each other. There are witnesses to everything that happens. They love and trust you. They know that you have fought for them. You describe pockets of clarity for your wife where she can be kind and understanding, where she does realize that she is out of her depth. Why would this not continue to be true? Won't you be there for them every time they reach for you? Won't you be there (keeping a record of course) every time she deviates from the custody because she can't handle the responsibility?
I think your lawyer is trying to tell you that even a fireman who runs into a burning building can't save everyone there. Sometimes we have to save the ones we can and hope that the others find another way out. Don't just accept this. Don't give up on the kids. Don't give up on you. Just get creative. So court is not going to give you what you think is right. How can you still be the best mom for those kids every single day.