What is the correct supplication to say upon entering the home if the supplication: "O Allah, I ask You for the best of entry and the best of exit. In the name of Allah we enter, and in the name of Allah we exit, and upon Allah, our Lord, we rely" is weak?

The aforementioned hadith was deemed weak by Al-Albani and others. There are two other hadiths, one authentic and the other good (hasan), that clarify what a Muslim should say when entering his home:

The first is narrated by Muslim from Jabir ibn Abdullah, that the Prophet, peace and blessings be upon him, said: «When a man enters his house and remembers Allah upon entering and upon eating, Satan says: 'You have no place to spend the night, nor any supper.' And when he enters and does not remember Allah upon entering, Satan says: 'You have found a place to spend the night.' If he does not remember Allah upon eating, Satan says: 'You have found a place to spend the night and supper.'»

The second is narrated by At-Tirmidhi from Anas ibn Malik, that the Messenger of Allah, peace and blessings be upon him, said to him: «O my dear son, when you enter upon your family, greet them with salam; it will be a blessing for you and for the people of your household.»

These two hadiths indicate the remembrance of Allah in general and the greeting of salam.