This sentence sounds a bit confusing and long to me. I might write it as follows:
Seeking to instill responsibility and family values in him, she discourages J. from alcohol and from emulating his own father's behavior. Thus, she paves the way for the ----- of the father in Brazil.
I think "regeneration" and "rebirth" would work here, but I might consider "improvement" or "renewal." They have subtly different meanings:
"Rebirth" and "regeneration" make me think that the fathers of Brazil are making a fresh start in how they act.
"Improvement" makes me think that they're working to be better fathers, but not necessarily making a clean break with the past; it's slower than the others.
"Renewal" is similar to "rebirth" and "regeneration" but makes me think more of a return to traditional values and roles.
I don't think "integration" would be correct; that would indicate that fathers weren't part of Brazilian society to begin with.
