A godparent is someone your parents choose shortly after your birth, traditionally it meant that they were to take care of you in case of your parents' death. More modern intent is that they are an adult you can talk to and look up to as you grow up to help guide you.
A godchild is someone whose parents chose you to stand in for them, as above.
There is no such thing as a god-sibling. "Godbrother" isn't even in the dictionary, its not a real word. And thats saying something; English is a language made up of made-up words and words stolen from other languages.
The children of your godparents are at best, "friends of the family" but there is no title for that. More likely they are just people you might occasionally see at holidays or family gatherings. I haven't gotten far enough into the story to find out how this "godbrother" actually relates to the MC, "child of godparent" is my guess.
...Ok, uh, reading a couple screens into chapter one and it is "explained" I suppose. If Tilly is the MC's godchild, then Tilly's parents are... (drumroll please) ...friends of the MC! Probably even close friends. Thats it though, there is no title involved. How has this game been out for this long and that hasn't been corrected? If this is an incest workaround, its worse than landlady/tenant.