She wept tears of joy when she heard her son had survived the plane crash.
Literal
She [topic-は] airplane-crash-accident [in-で] son [subject-が] life narrowly-escaped thing [object-を] heard [then-て] tears-of-joy did.
一命をとりとめる ('to barely escape with one's life') is a dramatic compound. うれし泣きする ('to cry from joy') combines うれしい + 泣き. A complex sentence with deep emotional content.