I guess it was the straw that broke this camel's back.
The point is grief is unpredictable. And finding out someone is dying is a form of grief. They might still be with you, but you know you're on a timer. You know everything is going to come crashing to an end.
Because it is so unpredictable, I don't think it's a good idea to tell someone over the phone unless there's any other way, and I don't think you should tell someone if they don't have adequate support around them.
In this scenario, the risk is he would struggle to hold it in around his child, or he would lean too heavily on his child. Parents are supposed to look after their children - their children aren't supposed to take care of them.
I am famed for holding it together and never crying. I still reacted badly. The OP's DH is known for not holding it together... Yeah, I'd wait. I'm holding firm on that.
Yes, he might be upset with the OP for not telling him sooner. That will pass. Whatever the OP does or doesn't do, there is a risk he will say something wildly unreasonable and awful. When we're in pain, a lot of us lash out with our words. We shouldn't, but we do.
I suspect MIL has told the OP so she can process the news before OP's DH - because MIL thinks he is going to need to lean on her heavily.