Answer
(Fatwa: 180/171/B=1431)
Yes, two raj?ee (revocable) talaqs will take place and husband can take her back within iddah period. Once the iddah is over and he did not revoke, he will have to perform a fresh nikah. But in future life, he will own only one talaq i.e. if he gave only one talaq, it will be the last irrevocable talaq (mughallazah) and they cannot rejoin except after valid halalah:
كرر لفظ الطلاق وقع الكل (الدر المختار)
وإذا طلق امرأتہ تطليقة أو تطليقتين فلہ أن یراجعھا في عدتھا، رضیت بذلک أو لم ترض (ھدایہ)
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband