I'm really surprised that reading at the table is considered bad manners. Up until around 15, I would read durring dinner, but it certainly did not stop me being part of the conversations. This was at home, though. We didn't eat out enough for me to remember whether I read then too.
I am a big believer in children being expected to behave, be polite and participate during events that they are invited / taken to. I also think it does them no harm to be bored every now and then.
I don't agree with electronic devices being used for entertainment purposes during dinner, especially when out at a birthday meal, irrespecive of the length of time they have been waiting. I suppose, by that same thread, I wouldn't expect them to be colouring in, playing with toys etc either: surely they are just versions of the same thing.
I wonder if children are used to needing these things as a result of parents wanting to keep LOs occupied while they discuss other things...maybe dinner time is not the time for these discussions? If you are all sat round the table together, a conversation in which everyone can join in is surely the most polite option?
I don't know how I will be with my DD when she is old enough to participate in dinners (atm she is 8 weeks old). But, I'd like to think that she will be happy finding her entertainment from those sat at the table with her, not a toy, gadget or book. However, I know one thing: she absoloutley would not be allowed to get down from the table to run/wander around or mess around under the table.
In your instance, OP, I would be making sure the DDs call their GM and apologise for their behaviour at her birthday dinner. The priveidges you have witheld from them would be witheld until the apologies were made. They embarassed you, too, with their behaviour, so if I were you I would expect an apology off them both too.