Does the mother's iddah end on April 26, 2017, corresponding to Rajab 29, 1438, knowing that the father passed away on December 19, 2016, corresponding to Rabi al-Awwal 20, 1438?

If the mother is pregnant, her 'iddah (waiting period) ends with the delivery of her entire pregnancy, as Allah Almighty says: {And for those who are pregnant, their term is until they deliver their burdens}. If she is not pregnant, her 'iddah is four months and ten days, as Allah Almighty says: {And those of you who die and leave wives behind, they shall wait on themselves for four months and ten [days]}.

The 'iddah begins from the time of death and is calculated by lunar months, except that the month of death is completed to thirty days if the death occurred during the month. So, if your father passed away on the 20th of Rabi' al-Awwal 1438 AH, her 'iddah would end on the 29th of Rajab of the same year (assuming Rabi' al-Awwal has 30 days), or at the end of Rajab if it had 29 days.

The calculation of the 'iddah begins from the moment of death according to the majority of scholars, while according to the Malikis, the day of death is not counted if the death occurred after dawn.