According to al-Jalalayn, there are two readings for 11:81....
they said, ‘O Lot, truly we are messengers of your Lord. They shall not reach you, with any harm, so travel with your family during a part of the night, and let not one of you turn round, lest they see the terrible predicament that will befall them, except for your wife: (read illā imra’atuka, in the nominative, as a substitute for ahadun; a variant reading has illā imra’ataka, in the accusative, as [her being] an exception among [his] ‘family’, in other words, do no take her along when you travel) lo! she shall be smitten by that which smites them: it is said that he did not take her along with him; it is also said that she did set out [with them] and turned round, and so exclaimed, ‘Woe is my people!’, at which point a stone struck her and killed her. When he [Lot] asked them about the time of their destruction, they replied: Truly their tryst is [for] the morning, and when he said, ‘I want it to be sooner’, they said: is the morning not nigh [enough]?’
The most common reading goes as imra’ataka while the other goes as imra’atuka. The former reading means that Prophet Lot's wife was exempted from salvation and that she was to be left behind. The latter reading on the other hand means that not any of them should look back except the wife. So Prophet Lot AS did took her out with him.
There's been some confusion going on but we are told that both readings are authentic and authoritative. Can someone explain how the readings complement each other?