I am sorry no one answered your post, Cathie, but I'm sure it's because it's hard to figure out what is going on with your uncle's situation. So I will try to take an amateur stab at this.
Has he been declared incompetent? Does his wife have guardianship or any kind of power of attorney? If not, your uncle should be able to get his own details from the nursing home and from social security about his financial situation. They may not be able to talk to you directly, but maybe you could try calling from your uncle's room and saying " I'm calling at the request of my uncle who has trouble with his speech, he is right here, can you explain to him..."
Another way to get information is to ask the relevant state employees general information questions about eligibility for nursing home assistance, social security payments, etc. , without making reference to your uncle's specific case.
The $35 figure is the amount that Social Security allows to be reserved for personal needs when an individual is in a nursing home situation, with the rest going to the nursing home. I can't figure out how your uncle's wife could be keeping the rest of it , I suspect she has to send it to the nursing home. If your cousins are minors then she would be receiving payments for their support from Social Security so perhaps that is what she is keeping.
I am not a lawyer but I remember reading some years ago that courts will not intervene in spousal support issues in an ongoing marriage as long as someone is fed, clothed, and housed.
The process of finding out what benefits people are eligible for, what programs are available, what their rights are can be exhausting and necessitate lots of phone calls. In getting assistance for my MIL, I kept a notebook of who I spoke to, the date and time, and what they told me. When someone said - as they often did - my department doesn't handle...., I don't know anything about....., I always asked if they could suggest a person to call who might know.