Aunt Fel, I understand your dilemma & it is a common one for families with autistic children who age out of the government funded programs for autistic children. The autistic student is often permitted to attend public school until age 21 when they are 'graduated', but more accurately aged out. The next step is sending them to a taxpayer funded (or possibly private or insurance paid) group home.
I am not familiar with the vocational rehab facility you mentioned, but one of the obvious issues for most families is simply how to provide the nearly 24/7 care or companionship that a nonverbal or severely autistic person may need. The easiest option is 'transitioning' the 21 year old from public school (& school provided aides) to a group home. I would think it's a tortuous position for any family to find themselves, & a potentially traumatic relocation for the individual - especially if they are unable to communicate.
As others mentioned above, you haven't yet provided enough details about your nephew, like what is his current level of abilities, say around the home. For instance, can he make himself a sandwich? If not, has he never been in the kitchen or seen a sandwich being made - or does he not have the fine motor skills to actually do so? How advanced or not is his ability to communicate? Also, what type & level of education is or was he receiving at school? Was he in special ed classes or mainstreamed? Did he receive the standard ABA training, or not?
You say his mother is not able to teach him life skills, but most public schools provide some vocational and life skills training.
Very importantly, what would be the goal or hoped for outcome from placing him at the subject facility; & what would be the expected time frame? (A year, six months, etc ..?) Would it be a permanent placement or a temporary living situation? If temporary, are you envisioning that he would learn & competently master basic life skills so that he would eventually be able to live independently (i.e.; alone)? Or upon completion would he return to the family home, or instead move to some kind of group home?
Is the goal for him to eventually obtain some kind of vocational job, or would he receive disability?
You write that he does not want to go? How do you know that? And in other words, how did he communicate or make that known?
Likewise, what would he like to do instead? Of course if he hopes to instead live at home, play video games all day & be waited on 24/7 by his Mom, well, wouldn't we all, lol! But that's not a viable alternative. If he thinks it is he is unrealistic, immature & selfish ... despite his autism.
I have a very bright & capable, non autistic 16 year old nephew who would like to spend his days playing video games & being waited on 24/7 by Mom. He is also unrealistic & immature (plus lazy, although a good kid!). He got that way from being coddled & spoiled. His parents are working on undoing that & yes it's difficult. The point is that some problems are universal, & not unconquerable. I am of the personal belief that anyone over the age of 12 with even half a brain can start to understand how life works if it's articulately explained & the consequences are experienced first hand.
Does he also know that even if he was able to remain at home, play games all day & be waited on ... eventually his Mom & Grandmother would pass away from old age & at that point he would be homeless ... living very uncomfortably on the streets with NO ONE doing anything for him. Within one day he would be quite hungry & cold.
So anyway, what are his other options (if any) besides the subject rehab facility?
Also, has he ever been exposed to any kind of Facilitated Communication or the tools used for same?
Hopefully my inquiries will help to initiate a positive & useful discussion. Meanwhile I applaud your love & concern for your nephew!