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It would depend, if Rodrigo is an eternal child, then it would be after Raditz and before Vegeta (As before Raditz Bulma hadn't seen the Son Family in a while).
This would enable him to be raised by Bulma and Chi Chi as Z and either GT or Super goes on, plus be able to play (and include spanker/spankee scenes, of course, lol) with most of his fellow kids through Dragon Ball Z/GT/Super history.
Another related idea to this I had long ago is this child Saiyan Rodrigo landing on Earth, but losing his memories somehow, and then Bulma and Chi Chi take care of the kid who can barely remember anything but his own name.
It would show how both of them have different raising styles, as I'd imagine Rodrigo would spend some days with the Son Family and some days with Bulma....
....And yeah, Bulma and Chi Chi would argue a LOT with each other on how to best raise Rodrigo, lol. Specially when he slowly begins regaining his fighting aptitude/love for battle, as Bulma is WAY more open to this idea than Chi Chi!