وَقَالَتْ لاُِخْتِهِ قُصِّيهِ
...
had We not strengthened her heart, so that she might remain as one of the believers. And she said to his sister: "Follow him."
means, she told her daughter, who was older and was of an age to understand things,
قُصِّيهِ
(Follow him),
means, follow his traces and look for information about him, try to find out about him around the city. So she went out to do that.
...
فَبَصُرَتْ بِهِ عَن جُنُبٍ
...
So she watched him from a far place (secretly),
Ibn Abbas said, "Off to the side."
Mujahid said, "It means she looked from afar."
Qatadah said: "She started to look at him as if she was not really interested."
...
وَهُمْ لاَ يَشْعُرُونَ
while they perceived not.
When Musa had settled into the house of Fir`awn, after the king's wife had begun to love him and asked Fir`awn not to kill him, they brought to him the wet nurses who were to be found in their household, and he did not accept any of them, refusing to take milk from them. So they took him out to the marketplace, hoping to find a woman who would be suitable to nurse him. When (his sister) saw him in their arms, she recognized him, but she did not give any indication nor did they suspect her.
Allah says: