Congratulatons on your new grandchild.
"I am glad they have DiL's mum there to help out, so not much point in my offering to help out practically at the moment, but I'll bet she would have made sure her own children were fully informed.
Please don't fall into this comparison trap between the two extended families. It quickly becomes problematic. Starts with assumptions (like yours) then competition breeds in, followed by anger and resentment. Totally not worth it.
I think I will give him until the end of tomorrow, and if he hasn't told them then, just send a loving text sayinig they are worried, and I will have to tell them on Sunday if he hasn't managed to by then.
I wouldn't do this if I were you. This is not your news to announce. They've already said that you should stay quiet about it and give them the opportunity to announce their own news, in their own way and at their own time. Respect that. If you go to mumsnet, you will realize how this is a supposed big thing for DILs. It may potentially cause a rift. I'm sure during your big event you can simply steer away from the topic and if asked respond by saying how your son is fine and will address any concerns, but you want to respect his wishes.
but we are a family, and all in this together.
Im sorry but you are not all in this together and you certainly don't want to find that out the hard way by disrespecting his wishes. This is your sons family and he's in it with his wife and child/children, so don't undermine a request that his made as the head of his family. I'm sure your intentions are great, but again its not your news to deliver, especially he's specifically asked not to.
will obviously be pushed as to whether the baby has been born, and whether mum and baby are okay. I can at least nod to that, after that it is up to my son, but I find it strange he cannot send one text.
You can't nod to either for one you don't even know if mum is OK at the time the question is asked, and two you can't nod that the baby is OK when you've been asked not to speak on his/her birth. Nodding is an act of confirmation of birth, which you've been asked not to do. You seem adamant to be the one to announce/share/acknowledge this birth, and it may not end well especially if DIL starts adding these to her list of offences only to be pulled out 5+ years later on how you stole their spotlight.
It's too early to break their trust over this. Wait, be patient, give them time and respect their wishes. They are the parents to this child. Respect their wishes or they simply won't tell you anything in the future. This isn't about you and your family. It's about your son and DIL as a family. You've received some great advice on here with regards to NOT announcing this news. I'd heed to it. Remember that this is NOT your news to acknowledge or share. Tread carefully and all the best.