Should you be allowed to leave work early/take day off if your sister goes in to labour during work hours?

I am a Nanny and work 4 days a week, 10 hours a day. My 19 year old sister who I dearly love and am closest to of any one in my life, is due to have a baby in 2 months. She has a very loving and supporting partner, how ever, has asked if I can be at the birth incase her partner needs to step out to take a breather or needs support himself.
Of course I agreed to this but needed to inform my boss of my want to go to the birth and thought that if I gave her 2 months prior warning that I may need to call in late for the day or call her to come home to her children so that I may leave to be with my family.
This conversation was discussed over the phone and her response was (after hearing my story) was.. "I am not in a position to up and leave my job over the next few months so unfortunately, I am not in a position to make you a promises".
The family I work with have no support from family and friends, only me. So if they can't leave work, nor can I.

I feel betrayed because... For all you parents out there... If you could afford to pay a nanny to look after your kids 10 days straight whilst you go on an oversears holiday. Would you? They leave me with their kids for long periods of time very frequently. I give up my life and put it on hold to make a miserable wage.

Should there be give and take in this working relationship?
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