How much should my wife charge my sister?

NO!  Family does not "do it for free".

Your wife should be paid what she normally gets for caring for an elderly person PLUS what a tutor would get for online education.  And if your sister makes six figures and ALSO now has Social Security Survivor Benefits for this child from his father's death, I see no reason why your wife can't be paid at least over $15 an hour plus.

And remember, when it is time for this child to attend school, by federal law, they must accommodate his disability.  And by state law, your sister is medically liable to get psychological testing and medication therapies from this boy's pediatrician for him and not just dismiss his diagnosis.

Remember that your sister has a second income for this child from Social Security Survivor Benefits so don't be shy about asking and demanding a living wage for the good care your wife is giving him.

maybe she should try to get custody of him

I would think $15 an hour is reasonable, but you’ll probably have to increase that after time. It’s hard for us to determine a cost when we don’t know what his day to day needs are 

That's for your sister and your wife to decide.  

I would suggest having your sister offer your wife a fair amount and if it's agreeable to your wife and yourself agree to it.

Since your wife is the person providing help, then the issue is between your wife and your sister.  Not sure what you have to do with it at all.  

$20/hr, tax free (under table) would be very cheap.

She should charge the same rate she charges when she watches the elderly, less 20% as a family discount.

"Free" isn't an option since it costs someone either way.  For example if you wife normally earns $400 a week doing it for "free" means it costs your family $400 a week.     Some people struggle seeing it that way, but that's the reality of real opportunity cost.   You will want to least break even on what she would normally be doing.   $10-$15 an hour is reasonable. 

You do not go behind your wife's back and give your sister a number.

You sit down with your wife privately and come to a decision together.    You want her to charge.  She doesn't want to charge.  The two of you need to work out your finances.  Married people are supposed to work together as a team to resolve conflict in a way that works for both of you.

Seriously.   If you go behind your wife's back and make a deal to pimp her out for money when she is in opposition to that, plan on needing a good divorce lawyer.

Has your marriage been happy?   Because it doesn't appear you have much respect for your wife. 

🥴 Um.... a reasonable price would be a livable wage. 

Start off with minimum wage. Because that in itself is a lot of money. Especially, if your wife would rather do it for free. 

Minimum wage you'd have to look up in your state. Mine is $12 an hour. Soon to be $15.

But in other states, theyre still at $7 an hour.

And just keep in mind all the chores your wife would be doing for the child. Does he have violent behaviors? Does she cook and do his laundry? Keeping his living area cleaned? Shower him? Those chores would call for a little extra. But just watching and babysitting or teaching him things? Would basically be minimum wage.

🥴 Edit: @ the other anon who is a dumba$s, the wife cant work for free. It will take a toll on her. She will become bitter and resentful. I know. Because I fvckin worked for free. FOR MY BLOOD RELATIVES. AND NOW I WANT THEM DEAD.

They took credit for my work, stole from me and ruined my reputation. 🥴 The husband is correct for looking out for his wife. She doesnt have the balls to do it herself. This will keep the books straight as no one owes anyone anything if sister pays for sister in laws services.

And @ hubby: 🥴 Make sure you get everything in writing. For future reference. Your wife and sister might need it.