Well, it sounds like it will be interesting.  How is your relationship with SS?

@ClassyNJ - try your best to remove yourself from the situation. I went through SKID wedding hype/drama/nonsense - you are damned if you do, damned if you don't. If in doubt, SIT IT OUT. Go through motions but the extra stuff? Mostly DIL and DIL's mommy will be running the "vision", just protect your wallet. 

As for DIL and DIL's parents stonewalling you...this seems to be the common occurence. Males of the family bond deeply with their wife's family and break off from their existing family. The inlaws really don't care to know you because you have nothing that they want and they already know they've got your son in their palm so...why even try? I suggest being cordial and leaving it at that. 

You may feel some frustrations pop up at how one-sided this deal is for SS but in the end - it's his problem, not yours. 

From what I remeber you've clearly laid out your boundaries - i.e.- when SS thought he would be getting a handsome inheritance from you - you directly and boldly corrected him. I would keep being direct and not get into any gray areas with the wedding stuff. If they ask for money or stuff or whatever - you make it clear what you are giving is a one time deal or if you are not contributing at all then be clear from the start. We ran into asking, asking and more asking - flowers flown in from thousands of miles away (that were not pretty by the way), extra special this and that- and then when the wedding essentials needed to be paid for DIL and DIL's family were quick to try to place it all on us. Our only saving grace was we took a strategy of paying for ONLY what the groom's parents pay for traditionally.

We put on a catered rehearsal dinner - absolutely gorgeous with fireworks to boot, grooms stuff,  paid for flower arrangements, etc- they really didn't keep a good budget and overspent (I had asked SS to create a quick budget and stated I would help him- he didn't and the whole thing was fairly disorganized.) 

So what did DIL's family do for the wedding? They served water and 1 cookie at the wedding (no meal, no nothing.) The reason I found out it was 1 cookie per person was I went up for a second cookie after 8 hours and the family running the stand told me "We saw you eat a cookie after the vows were exchanged, you're not permitted another one!" 

The irony is everything WE paid for was first class, DIL's family on the other hand didn't even hire a DJ they had our SS be the DJ. It was pretty interesting. It showed how one family was expected to really put out a great deal of resources while the other family felt entitled that we would cover everything and when we didn't they cut every corner imaginable - maybe it was to punish us ? But for the 300+ guests that they invited it reflected on them. To this day I typically avoid SS's rents - when I have seen them post-wedding they are typically screaming about the pandemic being a hoax, conspiracies left and right and spreading as much disinformation as they can discover from unprofessional news sources. I literally had to walk away when the DIL's mom started chanting bizzarro stuff in a parking lot after an event we were all at - she began demanding everyone join and I watched as SS, DIL and all these younger children from her different relationships were shouting her new chant. I looked at my partner and I didn't have to say a word...it was all too bizarre and that was the moment I released myself from feeling any type of way but indifference. 

Its awkward to say the least.   Both DIL's parents are introverted/very shy.  I can only imagine what they think of the boisterous Chef!  I have only made small talk with DiL's mom as they are very large and close knit family and seem to only associate with immediate family members.

Be confident, be radiant, and make this part of living your best life.  If FSDIL's family are the cockroaches they appear to be, they will run for the dark corners like roaches do when a light is thrown on in a dark roach filled room.

You and SS are close, Leverage that dynamic to stay close following the wedding.  Keep in mind that an engagement is no guarantee that there will be a wedding.  I My first engagement did not make it to a wedding.  

Keep investing in your relationship with your kid, the SDIL will get on board, or not. Either way, make you about your family relationships.

While some marriages certainly align the marriage more closely with the brides family, that is not a given.  My first marriage followed that model.  Mostly because my famiy was international and my XW and I lived in her home town. My XMIL was the dominant partner in that marriage, my XW tried that in our marriage. I am a product of a partnership marriage. So, XW trying to dominate was not how it played out.  Not that it really mattered considering her extracurricular activities.

I learned and never again would I call anyone mom or dad but my mom and dad, never again would I tolerate a marriage that isolated me from my family.  We have always been close though we have been spread across multiple continents.  My parents made our closeness an absolute regardless of geographic proximity.

We have never really had to navigate anything remotely similar to the dynamic in my first marriage IL configuration.  We met in a different State than my DW's family was rooted in and a different continent than where my parents were.  My parents retired to our city and built their retirement home between our home and my brother's a couple of miles from each of us.   My DW and my parents have an exceptionally close relationship.  Our marrital relationship with my ILs is good but the woman my DW has grown to be has little in common with her family.  Her epiphany, not mine.

So, bank on your family relationships, welcome SDIL if she actually makes the cut, and give SS the support of knowing his foundation family relationships are durable.

The variables in IL relationships within a marriage are an interesting study.  

Growing up, our family tended to be closer with my mom's family when we were younger. As we moved into our teens, that shifted heavily to being close with dad's parents.  In our marriage, my parents are SS's absolutely dedicated GPs.  My MIL and FIL for whatever reason generally do not get particularly close with their GKs or even with their own kids once their kids reach 18.  The SpermClan is a viper pit of manipulation though for some reason half of the SpermIdiot's spawn wallow in the pit, while two detest him and have some clarity and independence from that crap.  SpermGrandHag is the domineering matriarch.  Apparently SS escaping shook the foundations to that shit show causing some durable instability in the dynamic that was in place before SS wrote them off.  SS is not in a life partnership, He may never be.  His standards are so uncompromosing that I am not sure he can build a partnership that will meet his expectations.We may never need to get into the balance between ILs arena as Parent-ILs.

As parents of 5 kids, we've met 7 sets of inlaw parents.  On a compatibility scale of 1-10, they've ranged from 3 to 8.  (I wonder how they'd rate us.  Lol.)

I'm civil and polite to them all, regardless.  Some have continued to be in the picture, no death or divorce.  I know there's always the chance I'll have to be interacting with them at gkid events.  A couple of them have been wonderful Influences and helps in our kids lives, others are inactive.  Whatever but thanks for the good ones.

Paying per the traditional cost distribution can keep the drama down. If the Bride's parents want the princess bride extravaganza, they can pay for it.  The Groom's people cover the flowers (wedding party, church, and reception foliage), the tuxedos for the Groom's party, and the rehearsal dinner.

If... BIG IF.... both parties are respectful and reasonable, collaboration on a different cost distribution can happen.  However, any crap and ... nope.  Back to the historical cost breakdown.

My XILs approached my parents to split the cost of the wedding. My parents were amenable to that on the condition that each set of parents cut a check to both XW and me and we choose what to do with it. Buy a house, invest, wedding, or some combination.  Hell no. My XMIL told my parents that her daughter was having a top notch wedding. So, back to traditional cost application.  Karma... was that we married on Jan 2 at a Catholic Cathedral and the holiday arrangements were still fresh and in the Cathedral. So, that got my parents out of $Thousands in flower costs.  Meanwhile rip off her employer for even more and back at the ranch, XMIL charged a ton of crap to the business accounts of her employer, they remodeled their house to show off to their relatives from back East, got the business owner to do all of the meat for the reception, he is an award winning BBQ cookoff champion, and they tried to push me to provide all of the booze from my restaurant. Nope, can't give away ABC tagged liquor since it is taxed based on revenue for bar sales.  I probably started that marriage in an XMIL shit puddle now that I think about it.  Breaking the law was not something she thought a thing about avoiding. 24yrs later she went to Federal prison for embezzlement.

It could be a long wedding.  Everything depends on how crazy the MIL is going to be and the bride.  Expenses of a wedding can go crazy .  Just for party that lasts 4 hours.  There are marriage that break up before the wedding is payed off.   Try to stick to your guns on how much money you are going to give. Plus's 10% more.    
'Try to stay out of it as much as possible.  Because everything is going to be your fault.

GOOD LUCK.  CONGRATULATIONS