When my YSD was in 2nd grade.. she wanted to live with us.  My DH agreed to continue to pay CS to their mom.. 

When both the girls were in HS (at different times).. they both finished up living with their grandparents (my DH's parents).  This was for a variety of reasons.. first schools better.. 2nd.. fighting with mom (NCP).. third.. we lived in a fairly remote area ourselves.. and DH traveled for work.. so wasn't conducive to parenting full time.  Again.. he still paid BM.. and she would not agree at that time for them to live with us... so the next best thing to get them away from their mother's toxic home.. was to allow them to live with his grandparents.

In your case.. Legally, he is meeting his responsibility by paying CS to his EX.  It would have been better, I guess, to have his son live with him.. but for various reasons.. maybe that wasn't going to be in the cards.. (and in the end.. you probably are lucky).

Should he pay the grandparents?  well.. technically, he is paying his ex.. so if SHE is giving HER primary parenting responsibility to her parents.. SHE should be compensating... so I get him not paying double.

BUT.. for the driving school?  I think your DH should pitch in for these kinds of extra expenses.. directly to her parents.

So, for whatever reason things have slid down this slippery slope and youve lost the respect. 

If you do not have separate finances, I would consider separating them now. 

You can ask questions and be there as a support partner, but you cannot push him to "do the right thing" especially since you are getting pushback. Thats his deal, and you have to be ok with it. He probably doesnt want to upset the apple cart and if BMS aged parents are willing to do this and BM is not giving them the money, thats on HER. Hes paying his share, and thats all he can do. It would be an expensive endeavor to go through courts to manage this, as many on here have seen. So, just do the countdown like we all do. Then it wont be an issue. 

Driving class he definitely should help pay for. 

He has to give the child support money to whomever it was legally agreed to.  He doesn't want to go to court to have it changed?  Is he thinking if he gives the child support to the grandparents,  his ex will take back the skid to live with her just to get the $$ again? And he doesn't want that to happen?

I know there was a year when my S.O. had custody of his youngest son 24/7.  It was supposed to be 50/50 but the BM and step father kicked the kid out.  He wouldn't go back to court and just kept paying for a year until the kid turned 18.  He figured she'd want to switch back to 50/50 to avoid her paying child support ($ only flowed in one direction  in this situation and it was always to BM) and he'd just sold his business so his income looked really high.  He wanted to leave well enough alone.  Funny how that always works to the benefit of BM.  Seems they have these men trained to just hand over the $$.

Your DH does not owe his XILs CS. He owes his failed family breeding partner CS wich in all liklihood is clearly defined in the CO.

To stop paying the XW(CP) and start paying the XILs will likely put him in violation of the CS portion of the CO.

And... he should pay not one Cent more than what is COd as CS or other contributions (Usually half of medical bills not covered by insurance, etc....).  Not a single Cent.

CS covers DH's entire obligation for the support of his child and pays his X for caring for the kid when the kid is not with DH.  If XW outsources the care of that kid to her parents.... so be it.  As the CP, that is her choice and her choice alone.  Unfortunately the CP cannot be held accountable for how they spend CS paid by the NCP. DH's CS covers everything he owes, including driving lessons for his child. What BM spends it on, is up to her.  DH has zero obligation to pay his XILs.

We spent some money gaining this lesson when we attempted to collect for half of sports equipment costs, half of band instrument costs, etc... Nope. The Judge gave us clarity.  The CS is the NCP's entire obligation for the support of the Skid unless otherwise stipulated in the CO. In our case, in addition to CS, the NCP was required to pay 50% of any medical related expenses not covered by medical insurance, and 50% of long distance visitation travel costs. Each party was required to pay for the transport of the kid to their location for travel too and from SpermLand for visitation.

"Herein lies my problem"  You have the "(your) problem" part absolutely right. This is your problem and you are also making it a problem for your DH and for your marriage. When it is not a legitimate problem. Enjoy your relatively drama free blended family marriage. Do not stir up shit that does not have to be stired up.

So, stay out of it, learn the CO in totality, and ...... stop injecting drama into a situation that appears to be at a tolerable status quo.

I get that the BM is a POS.  But since her abdication as a parent in favor of her own parents keeps her out of your Cheerios, stop being a PITA for your DH.  Set and enforce standards of behavior and standards of performance for SS when he is in your home. You cannot rescue him from the shallow and polluted end of his gene pool though it is tragic that he is primarily being raised by the same people who created the POS BM.

IMHO of course.

Take care of you.