It was a great moment to make BM even more detestable by revealing that she really dosen't like any of her children much but it felt kind of meh for her to refuse help from her first mate.
I thought Perspero's father was her first mate.
I agree that Big Mom isn't quite getting the portrayal we've felt that a Yonko deserves to receive, but I think that its a good that Oda didn't opt to write her as being completely infallible so far. Otherwise it would feel more like an asspull when Luffy inevitably foils her plans.
I just hope that she gets a chance to stomp G4 (maybe even while weakened from Caesar's poison) before this arc is over. Other than offscreen-ing Brook, BM still doesn't really have any real combat feats, and that type of display is exactly what her character needs right now.
I am 100% sure if Big Mom even had Elbaf had her backing, she wouldn't of beaten WB regardless.