Niece's Wedding or Grandchild's Birth?

Daughter. Send regrets and a nice gift to the niece and don't worry about a thing.

Agree absolutely! Daughter is more important than niece, and your grand-baby is more important than a wedding!

Your daughter will shoot you if you miss the baby's birth. The niece will hardly miss you. You have a good reason for missing the wedding. It is not as though you are just blowing it off because you don't feel like going. As stated previously, send a nice gift along with your regrets at missing it. Maybe the gift can be a little nicer since you will not have the traveling expenses.

You could just flip a coin.

Also, where is the reception being held and what's for dinner? That might be a mitigating factor in vetoing a coin toss that favors a visit to your daughter's birth of your granddaughter.

If she delivers before, you might be able to attend the wedding, but the daughter should come first.

Which place will be serving the most alcohol?

They generally don't serve alkyhol in delivery rooms here in the US. At least, it's not covered under Obamacare.

Thank God for the NHS.

I wouldn't think of that as a choice at all. Since you ask, nothing, wedding or whatever, can be more important than a daughter and welcoming a grandchild.