She worked really hard while no one could be there.
「立ち会う」= "To be present", "To witness"
「頑張る」= "To try really hard", "To do your best"
「誰も立ち会いに行けない中」= "While no one could be present"
「彼女は一人でとても頑張りました。」= "She worked very hard on her own"
次の文:「このような状況下で出産した彼女を誇りに思います!」= "I'm proud of my sister for giving birth under these circumstances!"
「状況下」= "Under the circumstances"
「出産する」= "To give birth"
「誇り」= "Pride", "To be proud" = 「誇りに思います」
ご参考になれば幸いです。