So, the party's over and the result was...
...the day went down exactly as expected.
Mum enjoyed looking at all those old photos, even if she couldn't remember a lot of the people in them.
The two estranged kids didn't show, didn't send a card, didn't send a message.
Mum didn't ask where the kids were.
Everyone had a good time, including, presumably, the kids, because they chose not to come and they got what they wanted.
I would like to thank everyone who replied, because it is really helpful to get other people's perspectives on difficult situations like this, but so many people suggested that the kids should be invited that I thought I should explain, with the greatest respect, why I think this would be a bad idea in our specific case, and also generally.
Two years ago, our son's grandfather (my wife's mother) wrote a cheque for our son and asked us to forward it to him, which we did. There was no message from us, just his grandfather's cheque in an envelope. A couple of days later we got an email from the police saying that our son had made a complaint about us and that if we did it again it would be viewed as harassment and the police would have to take action. Faced with such a hostile response, we cannot take the risk of contacting him, even via a third party.
Also, have you seen the contemptuous language used by some EAC on their online forums? Family members who pass on messages from parents to EAC may be called "flying monkeys" (I believe this is a reference to the Wizard of Oz) or a "golden child" (if the messenger is a sibling).
Also, our non-estranged son is in regular contact with his two estranged siblings. We have never tried to prevent this, or asked him to pass on messages (for the above reasons), but he came to the party and it's inconceivable that he didn't mention it to his siblings on his own initiative.
Good luck everyone, and stay in the game.