You been trying to be the communicator in the middle of dysfunction junction. And both sides do not appreciate your efforts. Although I am surprised that your P actually spoke to his D about the photo. My H would never have said a word. He is all light and fluff with his D. 
Regarding the wedding. I would not say anymore about it. Consider yourself lucky and plan a great day/weekend for yourself. 
I would simply let the chips fall as they may. Don't discuss it. Don't even think about it. Life is too short. Honestly I've spent years chasing for approval and you Just can't win. 
 

Nutshell response here.

1.  You didn't need to contact his daughter about that picture.. whether it was meant rudely or not.. he should have dealt with it.. you inserted yourself.. and there is really no way that was going to go well.

2.  You don't like these people.. they aren't "family" to you.  I would not be at all concerned that I was not obligated to go to the wedding.. your SO can go as it is his daughter.. and either you can trust him to act appropriately with them.. defend you if needed.. or you can't.. in which case.. why be with him? or he can choose to not go if that is what HE wants.. I don't think I would give him any opinion or idea other than you are fine not attending but understand if he wants to for his daughter.

I agree that you are trying to do the communicating with his kids that your SO should be doing. Been there, done that. My DH is the same. Hates confrontation and overlooks way too much bad behavior. Granted, he's made huge changes over the years but in the beginning, the interactions you describe are much like I dealt with. So, definitely stop with the "trying to fix things." Both times you interjected yourself in your post, should have both been things your DH stepped up and took care of.

Now it's time to disengage. Stop all communication (texting, calling). Let your DH handle that. Start following the "civil but superficial" policy when his kids are around.....treat them like you'd treat the clerk checking you out at the store. As for the wedding, thank your lucky stars. You really did not want to go anyway and I'd just tell your DH she didn't need to put her snarky comment in the invite....you weren't going anyway. If he wants to attend, send him offf happily and plan yourself a special day. Heck, even a nice weekend somewhere so your SO can say, "Selly is at the beach with her girlfriends." OWN that day. If you are the gift buyer, stop that, also. Anything you are doing that a "mom" figure would do, STOP.  I'd also make myself "disappear" when they do come around. 

With that said, after 8 years, do you think your DH will ever change?? Are you willing to continue living the way you? Are you okay with these problems being around forever (as they usually are). 8 years is a long time with no change......

I hate the term "over stepping" but that is really what happened here. I realize you are trying to stand up for your relationship and for your partner but in texting his adult children, you have made yourself out to be the wedge in between them and their father. 

Like others said, disengage. Don't contact them again and IF they contact you, either ignore it or respond shortly and factually. No emotions- just yes/no type answer. 

Support him in going to his daughter's wedding. You spend the day at the spa- full day of pampering. De-stress and let it go. 

Stepping back is great, but the next time your reaction to their craptastic ways is to contact any of them .. DON'T! Nothing good will come of you contacting thme and it gives them fodder for their hatreds. 

It's his child, he should go but you shouldn't sit home. Make plans for a girls day/night out and live it up. 

Anytime I get inside a conflict, I live to regret it.

Steplife sucks. If you were married, it MIGHT be a different thing, but there are two camps, the first camp is "your partner must have you by his side, because you are life partners and to not invite you is disrespectul." The other camp is "disengage and live your best life for YOU. Dont let them "live inside your head rent-free".

In this instance, I have to say that you set yourself up for failure those two times that you have described. When the "are you two cute together" text prompted a response from you to adult SD, and when you texted his kids and took them to task for not having a decent non-transactional relationship to their father.

It was never going to go well. Thats just the way the ball swings in steplife. We are good for anything money or help-related but zero parenting. Its your partners choice to give money and continue with his ATM transactional relationships. Husband over here - when SD23 Feral Forger cant get what she wants/needs by mooching from someone will occasionaly call her father. She called briefly for fathers day. He moved her from 3 hours away...and cleaned it up for her. That was ALL him. I just made sympathetic noises.

Which I suggest you do when talk comes up regarding the wedding. SD is ok to put her hand or for money, yet disrespects her father and her fathers partner. HE chooses to accept it or not. HIS choice. Do not feel discounted, because you get to do you. Leave her to her misery of herself.

Be happy you arent invited.

You already know how dysfunctional they are. Any type of celebration the toxic clan pull out more toxic. Weddings are their playground.

Besides if you werent invited, why the F would you want to be there. I get it hurts. But lady the proof is in the pudding. They love to exclude and a wedding is their perfect opportunity.

Be kind to yourself.

I would if I were you.

Hit a nice boutique for an amazing outfit, get a makeover and a rocking flattering hair style.  Be radiant, and be on SO's arm beeming your happiness. Those who are toxic and manipulative will scatter for the shadows when you enter radiantly on your SOs arm.  Like cockroaches who run for the dark corners when a light is turned on in a dark roach filled room. Let the roaches scurry.

A parent of the bride or groom should not tolerate being isolated from their own mate by failed family historic baggage or issues.  Even when it is the wedding of that baggage.

IMHO of course.

For 3.5 with 2 kids aged 1 & 2.5 when sd's both decided to reconnect with their dad after a 5.5 yr disappearing and cutting off all contact. 
 

sd's were 13 and 23.5 when the eldest contacted her dad by txt message. This was followed shortly after with random pics of dad whilst married to her mum with a message "just happened to find this pic when you were younger and married to mum" like he was so happy yet the truth was their 16 yrs pf marriage was pure torture.

this continued a few more times, followed by pics of airport arrival hall and telling hubby she was there waiting for her mum and affair stepdad (yup they both had an affair before even separating from their exspouses) so trust me, my husband hates her with the fire of a thousand suns.

sd would then repeatedly message my husband that her mum reckons her marriage won't last long etc. my husband refused to answer any of these messages and it took him another 1.5 yrs before telling off eldest sd that this was inappropriate.

that they had both remarried and my husband had happily remarried and was building a future with me and our 2 young kids and that any crap of bio mum was not of his concern and he did not want her mentioned ever again. My husband told her it was incredibly disrespectful to me and our marriage that sd continue with this crap. 
the most hypocritical thing is biomum can whore around with affair stepdad and marry him whilst skids were at school and didn't even know their mum was having an affair etc yet 5.5 yrs post divorce, hubby is guilted for marrying me and even at the 8 plus year mark.

eldest sd fake cried call dad claiming he abandoned them to marry me and have 2 kids with me who were 2 & 3.5. Reality is they ended contact with their dad and i'm a convenient scapegoat

Sd's went no contact as usual. Now eldest sd goes no contact and will out of the blue send a picture with no message no hi, just plain rude and disrespectful. 
 

i refuse to be at any meets or family events sd's are at. Every prior outings they'd wear black when i was there. When i and our 2 kids aren't there, instant colour. Its like this miniwife crap where they fake mourn daddy married his so called half naked christian whore. Yup, batshit crazy exwife called me that. 
 

my husband even told his 3 kids from exwife that nobody wants to be around disrespectful miserable people and how they behave makes him not want to be around them and in the limited free time he has, he's made it clear he will not shuffle between our household and theirs because they refuse to be inclusive and just wanna be petty.

ss has come a long way, but sd's are just like their mum. Eldest sd is just like her mum and younges sd follows eldest sd out of fear and allegiance 

disengaging means i cut off sd's ability to report back to biomum and stepdad about me and our kids, it prevents them interfering and attempting to destroy our marriage. 
i have wondered when sd's marry if hubby would attend. He knows biomum can't be trusted along with her abusive narc family amd she would definitely cause a scene. I have a feeling hubby would tell his son to step in his place instead. But we'll see when the time comes

Id rather stick a needle in my eye than go to a skid wedding where toxic BS is the theme

Do something nice and fun for yourself instead. Life is too short to waste time on people who do not want you around.