Has your SO asked if you can bring them? If it isn't a super fancy affair with assigned seats it might not be that big a deal. If your SO is the best man, i'm guessing he is close enough to the groom to ask him about it. Also, though, if you are a week from your due date it may be a non issue. 

Get a sitter and go to the wedding if you are up for it. I wouldn't read too much into this. Weddings are strange things and there are many reasons why your kids didn't get an invite they would make total sense to the bride and groom. This is far from a hill to die on. And honestly, what kids would really want to go this wedding anyway - to most kids weddings are boring.

If it were myself I would go without the kids. 

However if you're due in a week it will depend on how you are feeling too.. 

No kids is no kids.  
 

So, no kids.

You should go, if, it is local.  I'm more worried about the proximity to your due date than the kids element of the situation.

Your SS is in the wedding.  Your BK's aren't.  Though one may be born at the wedding.

Keep it simple.  This is an adult event.  Get a sitter.

Congratulations on the baby.

Many weddings today have a "no kids" stipulation except for the ones serving in the wedding. Or maybe they only want kids there they know??? This is not a slight to you or your kids....it's what the bride and groom want.

Attend the wedding, if you feel up to it, getting a sitter for your kids. If not, let your SO attend with your blessings.

I think it sounds like a nice date night for you two. will someone be picking up your ss after them ceremony and pictures? get a sitter, enjoy it!

Where they don't know anyone .   Wedding aren't for kids.  Parents take them because it's easier to take them then find a babysitter,  expeccialy if it out of state. Traveling. Most of the time spending the night 

It's close to your due date. If you are feeling up to it, get a sitter and go. If you are not, stay home.

Weddings have budgets. Your kids did not fit into the budget. Accept that.

Your kids not being invited means SS won't go when he isn't invited.  There extended family events where this will happen. Facts of blended life.  So don't be butthurt over this.  Just because you have to accept SS , that doesn't mean everyone else has to, although it's extra nice when it happens.  
 

Enjoy you last night out as adults.  

Weddings are out of this world expensive, and you dont know the financials of the people getting married. More and more I see "no kids event" aka "adult only event" and it makes sense. But you are super close to your due date..that to me is the main consideration. So go have a nice evening, get the sitter.

get a sitter and go have fun. and remember to tell him well ahead of time that you will not be wrangling, feeding, chasing, or watching his son. that's his job. 

TBH, I am actually quite surprised your SO is asking you to commit to attend this even when you will be so close to your due date.. and that he hadn't put his friend on notice that there is a not too small chance that he, himself would not be able to attend.. and his son wouldn't either.. if you have had your baby by that time.

Have you asked him what the plan is if you have your child prior to the wedding?  

As far as your kids not being invited.. I would guess it depends on circumstances.  Are no other children invited except for the participants in the ceremony?  If other families are having kids included, I would think it a bit odd that his "best friend" would not think to invite his long term partner and her children as well.

Yes, I get that guest limits can be limited due to cost.. but in the end, having a couple extra children should not be the high cost addition an extra couple of adults would be.

So, if this is a more adult affair.. get a sitter.. or better yet.. tell your SO,  he needs to plan to go alone because you won't be up for a big day/night so close to your due date.. it's really the truth.