Sorry (not,), but there's no way I would agree to this.
It sounds as if they are openly saying that they definitely dont want you there, except to look after grandson during the birth of the new baby.
If you lived nearby, that would perhaps be be acceptable and doable, but you dont. You are expected to drive all that way, arrange and pay for your own accommodation for an unknown length of time, and could turn out to be several weeks, just so that you are available to look after their son for a few hours, then clear off back home again the minute that job is done?
This is a family who haven't visited you since the first child was born!
There is no way I would do it. I would be telling them to arrange for a private childminder to be available when the time comes! If they had so little consideration for me and their dad / stepdad, I would be prepared to live with the possible consequences.