Yosef's wife's story
There are a few differences in detail in the accounts, though basically, the family of Yaakov did not want this child in their household and insisted on her being cast out. Yaakov fastened a necklace with a kind of amulet that identified her family origins to protect her. That's what she had on her when all the women in Egypt set out to see the handsome young viceroy and threw over their jewels, so that's what she threw out to him. He read it and realized who she was and thus found his bride.
It's very fairytale-like: the abandoned child grows up to marry the prince and even has the key accessory (the amulet rather than a glass slipper here) that attests to her identify. So it has a kind of narrative appeal. That's why this Midrash tends to be told to even very young children despite the fact that there is very little in the text that points to it. But what they are not told it how these details actually point to parallels between Osnas and her husband, as well as to another future leader, Moshe.
Like Yosef, Osnas was cast out and left on the path that would bring her to spend the rest of her life in Egypt with no one who knew her background. Doubtless, the shvatim considered it right and just to abandon this child whom they regarded as mark of shame just like they considered themselves fully justified in selling their brother who appeared to plot against them. Ultimately, they realized that they had been wrong about Yosef, but did they realize the same about Osnas? Both the text and the Midrash do not address that question.
One other thing I was considering, according to the Midrashic identification of Osnas, it is possible to count her (rather than Yocheved as Rashi based on Chazal does or Yaakov as Ibn Ezra does) as the one addition that raises the count of 69 descendants of Yaakov to 70 in Egypt. Yosef and his sons are the last ones to be counted, so it is possibly hinting at her inclusion in the round number. Yet, if she had been disowned, perhaps she is not seen as making the count.
To shift back to when she was left to her fate when she was very young, according to one Midrsahic take, an angel looked after to keep her safe until she was taken into Potiphar's household. In Chizkuni's commentary (cited by Rabbi Joshua Hoffman here http://yeshivasbrisk.freeservers.com/Netvort/bereishis/mikeitz/Netvort%20%20parshas%20Mikeitz%205766%20%20.htm) That angel is identified as Gavriel, the same one who is identified as the ish who tells Yosef which way to go when he seeks his brothers. So the same angel is the one who leads both Yosef and Osnas to Egypt where they will meet and marry many years later.
But that account also harkens to later Midrashim about angels watching of the Israelite babes who have to be sent out of their homes because of the Egyptian decree on male infants. In fact, there is one particularly famous male infant who offers a striking parallel to Osanas' story because he, too, was adopted by a prominent Egyptian and rasied in that household rather than by his own parents. Of course, that's Moshe.
Another parallel image with Moshe is one account of Osnas that explains her name as a reference to a sne bush. In that account, she was not an infant but a bit older and hid herself in a bush when cast out of Yaakov's house. The sne image is striking, given the prominent role it plays at Moshe's first revelation from Hashem that he is to have the mission of redeeming his people.
I still find it troubling that Yaakov would allow his granddaughter to be abandoned in that way. In fact, when reviewing some of the takes on the Midrashim, I found a comment that encapsulated exactly how I felt about it: how could someone with the rachamim of Yaakov show such coldness to his own flesh and blood? However, that comment was on a take that suggested that Osnas was not Dina's daughter but Dina herself who was cast out and ended up adopted (as she was very young when attacked by Schem). That commentator rejects that view in part because he could not accept that Yaakov would send his own daughter away. But what of his granddaughter? Even according to the view I've heard that she was not regarded as of the family because her father was from outside the fold, I find it problematic. I can only accept it as another manifestation of the confusion of what is right that prompted the brothers to sell Yosef.