I'm glad I didn't have my baby when you were away from the hospital.
I'm glad I didn't go into delivery while you were on vacation.
ーI'm glad I didn't have my baby when you were away from the hospital.
「先生が病院にいない間に赤ちゃんが生まれなくてよかった。」
ーI'm glad I didn't go into delivery while you were on vacation.
「先生が休暇中に産気づかなくてよかった。」
「赤ちゃんが生まれる」は have one's baby と言えますが、
go into delivery
go into labor
を使って「産気づく」のように言うこともできます。
「休暇中」は
away from work (この場合は the hospital)
on vacation
のように言います。
ご参考まで！
カナダ 
