Sad,
Your DIL is totally unreasonable. DS may have told her any dumb thing, in order to try and create empathetic parallel tales of woe, to match hers. "He's a survivor." Yea. Tough guy survived your mother's free rent and having you launder his shorts and serve his supper for the last 25 years.
DS invited you to the wedding because he wants you at his wedding. When times comes, he may invite your DH and daughter anyway. Invitations have not been sent. Real plans for the one lousy night are probably not made yet. Is DS and DIL testing you "we decide who we want" to see if you'll "respect" their decision.
I read your 1.- 4. and all it seemed to me was a little cranky at most, which should not have been given past a moments thought, and nothing personal at all you did. Plllease~ changing a dirty diaper, mildly sarcastic defensiveness about dirty diaper, and making a bath joke out in the open. Okayyyyy. I'm in trouble myself if sarcarsm needs medication.
Your DIL sounds very immature. No matter her age she's young. Hopefully with time she will wisen up. New mama bear. My cousins all get very serious for a few years, but they do chill out especially after #2 comes. For now, next time you interact with them, stay so calm with talking to either of them. Do not bring up the past as it's not helpful when they do. Do not escalate. Shift the subject. Do not take verbal lashings of any sort from DS or DIL. Call yourself from another phone to have to take the other call, just get off the line. Politeness will get you through it.
Did they want more of an apology? Write out some bs one only if you feel like it.
Oh -- and if you've already kissed it goodbye, when the wedding actually comes give them a $100 check and a short note forgiving the total of his loans as their wedding gift. Just kidding. Kind of.
As a DIL I tell you, your DIL's very immature right now. Stay calm and ride through it.