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So Dom Pedro II was overthrown in an incredibly avoidable coup against him (most of the people involved didn't even realize they where De-throning him and would probably have listened if he had given the order to stand down). Unfortunately for Brazil in general Dom Pedro had grown increasingly tired of being emperor of Brazil and had little hope for the future of the empire due to the fact all of his sons and grandsons had died by that point.
So how bout as a POD we have Dom Pedro gain some measure of hope for the empire during the time he is away in Europe and she is acting as Regent, it's not like she didn't do much given how in her time as regent she effectively put in place the process by which slavery would be abolished. From there he can atleast feel more active in trying to stop the empire from falling. (Or in the very least he comes to an agreement that she takes over as permanent regent while he continues travelling the world under an assumed name since despite Pedro's expectations she'd probably be a fine empress)
From there the coup is either butterflied away or defeated early on, happens after that?