Answer
(Fatwa: 1182/1175=J)
If the talaq-letter is written by the husband or the husband signed it after listening it, then her wife is divorced with three talaqs and now she has to stay in iddah (waiting period). If the divorcee is not pregnant she has to observe iddah of three menstruation period; after passing three menstruation cycles from the talaq onwards her iddah will come to an end: والمطلقات یتربصن بانفسھن ثلاثۃ قروء (الآیۃ)
As far as taking her son to hospital is concerned it should be done by her brother or any nearest relative. However, in case of emergency she can take her son to hospital for treatment:
واما الخروج للضرورۃ فلا فرق بینھما کما نصوا علیہ (الدر المختار: 5/445، ط زکریا)
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband