DH to DGP, on phone. Enthusiasm and excitement can overshadow content or lack thereof.
"Papa? Come over! The baby's here! No, we are home; we never went to the hospital because the midwives never said to go and it seemed to go so fast once it really started -- Papa, we have a BABY. Come see!" (Engage in F/S male bonding until the baby and Alis are ready for a brief visit. DGP can now help out with housework and subsequent Toddler care to his heart's content and everyone's benefit.)
"Papa? Great you called. Alis is in labor. No, don't come over. There is a nurse taking care of Toddler, and there are just so many people (women) with the midwives and all, I don't know how we'd talk. The phone is better. Oh, yeah, that is how they do it now. There is no room at all in the house (for us men) -- let me call you in a bit when I know more. I am not sure where we will be or what I will need. The midwives are here, and we leave when they say to and, Papa, this is just so cool! Gotta go, nothing's wrong, by Alis is calling for me. Call you back as soon as I have news. Or if I just need to talk. Papa, please stay right there so I can call you when I need you -- and I will (because this is all woman stuff and I am kind of on the sidelines) so please be right there for me. I will keep you posted. Bye!"
The optional, or perhaps implied, "women stuff" language, admittedly sexist, is included because it might help DGP relate to the births of his own children, when he was likely completely excluded from the process. Pointing out that DH doesn't know where they will be (true) and he wants his father to stay right there where DH can reach him, to support DH (man stuff) may make DGP feel more comfortable and also keep him out of the way by giving him an important job -- supporting DH -- until the first one becomes the truth. DH will likely be grateful, and want to step out periodically to talk to his father. It can get a little, uh, female in there. I think DGP just loves the heck out of OP and DH and FGC and wants to be involved for that reason. No reason to be unkind just because he is old fashioned and maybe not expressing it in the most graceful way. Acknowledge the love, and just say things have changed.