If you can't see that there are multiple issues in play simultaneously, I'm not sure I can help you. Presence is one thing, and of course, is most important by far.

I'd like to be present for the birth, but also for my kid when he breaks an arm or has the flu. An increasing number of employers let their people do those things without losing pay, of they have sick time available. If you think that's to much to ask for, don't ask or don't vote for it. Management will love you even more!