I honestly think that I would not have had a fourth baby with him while things were like this, if it were so upsetting to me. (When I got married, I wanted to take a couple to a few years to get our relationship established, get into OUR rhythm and make sure that our bond was strong enough and ready for the things that would come next.)
Next, I think that I would have no problem hurting their feelings or disappointing them, if he weren't willing to do it. In response to the e-mail, I might have replied to all (following whatever rudeness they exhibited at your house) that this event was not set in stone so they should not save the date. Or maybe I'd RSVP that baby and I would not be in attendance, as we would have a prior engagement, and leave it at that. I wouldn't drag it out. If the date were closer, I might even have fun ignoring all the details concerning the event, until someone spoke directly to me about it. At that point, I would claim ignorance. I would let my husband know that either he can tell his parents that baby and I will not be participating or he can let them figure it out when we don't show up. Since they didn't consider consulting you, you have no obligation to address it with them at all.
There might be a cultural difference between us, so I don't know what options you actually have, but I wouldn't mind fighting with my husband on this. Things are out of order in your house, and I think that you have probably given him little to no reason to get things lined up as they should be. At this point, the tone has been set and patterns and dynamics created. You helped to lay a foundation where you and hubby are not partners. You're the only one who has a problem with the current status, so YOU will have to change it. You can probably start with a sitdown with him explaining that you started off wrong and need to get you guys on track. If counseling is an option, get in there. It's not going to be easy, because you'll be seen as going back on your word--unspoken word that this is all okay--but explain to him that you need this in order to feel important to him and at one with him, which is necessary for you to be the best wife and mother you can be. Be firm, but allow the occasional slip-up if you can see improvement.
ETA, following your SWH: I'm curious to know how he replied to you when you discussed with him this change. It sounds to me like there was good reason for him not to have been in contact with her. (Did you guys discuss THAT, by the way? It could have helped prepare you for what you're dealing with now.)
Instead of being mad at him, try to understand that he likely married you to be his champion in areas where he is just not strong. He can't stand up to his parents by himself. His first solution was to distance himself from them. Then, he thought that you might be a good buffer. Instead, they've come in and taken over again. By all means, feel free to speak up on behalf of your household. It might give your husband the courage to do the same.