There are stories of someone who had adopted a child and when they grew up married the son or daughter of the adopters. However, I do not think it was a normal event as a formal adoption. In talmudic times, one or the other would stay with the in-laws during the year between kiddushin and nisuin, but again it was not a formal adoption. In the Torah, if somone "purchases a Hebrew maidservant Mishpatim 21:7-11 as a minor, she must marry either the master or his son when she comes of age or go completely free.
The situation that you mention does not seem to be considered as a formal matter. Note that even if it was done, this would not effect the laws of inheritance.
[Shir Hashirim 4:10] (http://www.chabad.org/library/bible_cdo/aid/16448#v=10&showrashi=true) uses the idiom אֲחֹתִי כַלָּה to show love in all of its manifestations as well as the closeness of the relationship. This is used as an allegory for the relationship of Hashem and Yisrael as the either brother and sister or husband and new bride. The use of the two gives context to the closeness and naturalness of the relationship.
Note that since this is allegory it is not a formal legal relationship. However, people are to regard their in-laws with the respect due to parents.There are cases in which the husband of a daughter who has no brothers agrees to use the family name of her father so it would not be lost. However she inherits from her father by Torah law (Bnos Tzelafchad as an example).