We paid our kids an allowance of 20 dollars ever two weeks...seems low, but 40 dollars a month for:
Taking out trash
Loading/unloading dishwasher
Cleaning their bathroom/keeping it clean throughout the week
Helping with yard work on the weekends
Take out the recycle
Dusting
Vacuuming
Mopping
We had three kids in the house at the time so they would rotate jobs, like BS would take out trash one week so Spawn would load and unload the dishwasher. BD would dust and vacuum.

First, I think that kids getting an allowance is a pretty normal occurance.. but, usually kids have some level of responsibility in the home as well.  This can get a bit skewed in the stepland in a variety of ways.

First, how many days a month does he spend in your home?  If he is only there 3/4 days a month then the expectations for chores etc.. would be somewhat different.

Second, is he already also getting an allowance at his other home too? There is no reason to double up, and over compensate just because his parents are in different homes.

Chores are not the only way that kids should be given credit too.  Behavior and school performance are also their "job".. in fact, school is the equivalent to an adult's job for the child.  Second is maintaining their own cleanliness.. both of their person and their surroundings.  Finally, contribution to the home they live in is the final level of input.. helping to unload a dishwasher, clear the table... vacuum the living room, help mow the lawn etc... 

Growing up our allowance was a set amount and didn't require hourly contribution to chores.. but we were expected to pitch in and do things when asked.. for normal day to day type activities.. we also were expected to do well in school and to keep our room neat.  We might see a reduction or elimination of an allowance as a consequence for poor behavior.  

There was an additional layer of participation that would net us additional money.  The joke in our family when asked to do a new task was if we were doing it for "love or money".. ie was it part of being part of the household and our normal allowance limits.. or was it "extra" and would we get extra money.

In a situation where a child is in the home not full time.. I think that the regular set allowance should take that into account.  What types of expenses would the child normally have while they were in your home?  Movies? buying candy.. or other types of misc spending?  The kind of stuff that your DH is probably just handing out when he is asked?  So.. if the kid is only over 4 days a month.. certainly a set 20 bucks for the month as long as he keeps his room clean and maintains behavior standards including schoolwork.  That might include him being agreeable to unloading the dishwasher or taking out trash when asked.  If he is in the home 50/50... obviously.. money would be more.. but so would the basic chore expectations.. perhaps a regular responsibility in addition to the minor asks like clearing the table.

But, the boy also needs to understand that now that he gets an allowance that the freely open wallet stops.  He gets this money and will need to budget for himself.  Dad won't be constantly opening his wallet for every request.    That doesn't mean dad will never treat his son to something nice.. just that the point of the allowance is to teach responsible money management.  If the boy has extra grandiose wants.. then dad can come up with "extra" chores to allow the boy to earn money.

I don't know that your husband can insist he keep his money in your home.. but he can also not give in to requests.  "I gave you your allowance last visitation... if you took that home.. I'm not going to give you more.  that money is meant to pay for these things you want when you are here. If you took it to the other house.. I'm not paying you again.

I wouldn't pay by hour, but by chore. Unloading/reloading dishwasher could be $1 each day he does it. Vacuuming the house would be $5 and only needs to be done once a week. You get the idea. There are a number of ways to keep track of what he does, and DH can pay him weekly or biweekly like a real job.

As far as keeping the money, it would be better for your DH to take SS to set up a bank account (there are youth accounts available) and then see if SS can get a debit card for that account. If he can't get a debit card, then DH needs to be on the account, pay for SS's thing, and then transfer the funds from SS to DH (my friend does this with her kids who are younger than your SS).

ETA: We differentiate "daily chores" and "extra chores" based on whether it benefits one or all. Doing your own laundry isn't an "extra chore", but washing and folding all the towels and bedding for the household is extra. Vacuuming and picking up your individual room is daily, but vacuuming the whole house would be extra. I wouldn't pay big bucks to do those things, though.

I never got an allowance growing up. I would get money on birthdays and Christmas from various relatives but that was it. I don't think kids should get paid for doing household chores that you don't get paid for. For example, you don't get paid to make the bed, prepare your food, sweep the floor, etc. I feel like those are basic household responsibilites kids should be taught to do. I would pay for any "extra" work that is outside of regular up keep. Maybe paying him to mow the lawn? Wash the car? 

My allowance was $5/wk until I was 17.   If I wanted money beyond that, I had to earn it.

Not that I ever wanted for anything. We had a nice home, good food, nice clothing, etc, etc, etc.... but.... money for personal purchases we had to earn.  Usually mom and dad would make a deal with us. If we earned half of the money for what we wanted, a new bike, etc, etc, they woudl match it.  This developed in us the drive to earn as well as an appreciation for what it took to save for it and an appreciation for mom and dad's contribution.

IMHO it is critical for there to be a separation between what is earned in dad's home and what is earned and kept at mom's home in a blended family situation.

This prevents one parent from dominating the dynamic between each parent and the kid in failed family situations.

I would say that there should be no more of the Skid taking money from your home to BM's unless he earns it at an outside regularly scheduled job.  Initiating the he accumulates half and you and dad match it model will drive him to start to migrate his saved money back to your home and out of BM's control.

There should be a clear separation between the two homes, the resources associated with those homes, and the influence of the adults that lead those homes. For damned sure that kids should not be the ones in control.

As for chores... chores are the contribution that a child makes to the home.  They chould be used neither as punishment nor should a kid be paid to do them.

Cleaning their room, doing their laundry, cleaning bathrooms, sweeping, mopping, dishes, etc, etc, etc... whatever is appropriate for a child based on their age and capability.

Compensated jobs in a home should be for things like cleaning out the garage, tilling the garden, brushing cobwebs off of the house, trimming bushes, etc, etc, etc..... Kids who do these things and are paid fairly for their efforts will get jobs from neighbors, and will be compensated increasingly for the services they provide.

This is how I got my 10Speed which I traded to my dad for my BMX bike, how I bought my first guns, took trips that I wanted to take, etc, etc, etc....  I understood what it took for me to earn and save for those things which gave me a clear understanding of what my parents did to provide for our family and contribute to my dreams and goals.

A kid who does not do the chores that they should does not get compensated for doing the things that would otherwise earn them money, they are not rewarded for those basic contributions to the family either.  They are fed, housed, clothed, etc... for their basic contribution.

If they refuse to contribute, their access to the enjoyable aspects of family membership are limited as they grow up and gain the congnition of the consequences for their choices..

IMHO of course.

Our kiddos don't get paid for things that benefit mostly them. For example I don't pay them to clean their room and take a shower. 

They get paid for chores that benefit the home such as dishes, taking out the trash, and vacuuming. 

They get 10 a month which is pretty good since they MIGHT spend about an hour a month on those kinds of chores simply because we only have every other weekend and dishes cant wait two weeks.

They get extra for REALLY good report cards or if they get a special award at school like student of the month.

I agree with everyone on getting a bank account.  When YSS came to live with us getting him an account was a nightmare becuase he was over 16 and subject to the bank "Know Your Customer" checks.  He couldn't get a drivers licence due to his epilepsy so didn't have to photo ids.  He didn't have any bills in his name or any other proofs.

It was finally sorted when my DH mother remembered that she'd opened a savings account in his name when he was born.  I'm not sure what we would have done if she hadn't saved the day.