I don't know the word "extant" but based on my quick look in the dictionary, it seems redundant to say current extant, or extant nowadays (and nowadays is too informal for this writing) so just pick either current or extant. I would use acceptance. There are many thing people accept without overtly approving. "Scene" is too informal as well. There are too many colons used - you'll have to rewrite a bit to get rid of some of them.
Here is the summary:
This monograph attempts to show the reality of a current and polemical topic in Brazil: infant adoption by homosexual couples. To better understand the topic, first, there is a brief history of the evolution of family patterns and the changes that have taken place in the Brazilian family are discussed, showing the current new extant patterns nowadays. The next chapter shows the acceptance (or approval ?) of homosexual unions internationally scene and in Brazilian juridical system. There is also a brief study of the prejudice with regard to the towards homosexuality in the course of history, with the equality principle prevailing. This chapter [is this still chapter 2?] discusses the adoption problem in Brazil, as well as its requirements and purpose: to ensure the child and adolescent’s right to the family and community environments.[Not sure what that means]
In the final chapter, the core idea of this monograph is reached: adoption by gay couples. First, it addresses the problem that has permeated most of the adoptions by homosexuals in Brazil: when a homosexual couple wants to adopt, one of the partners has to be chosen in order to formalize the petition for adoption (formal petition), but, in practice, both parents raise this child. It becomes evident that the bond between the child and the partner of his adopter doesn’t find a proper juridical custody (a proper judicial solution) that preserves the best interests of the minor. Also, the monograph discusses * the legal possibility of homosexual couples adopting jointly, presenting studies about adoption’s psychological viability by these pairs and giving an account of the first favorable judicial decisions to adoption by them.
Your "adopting jointly" is fine.