Big Mom seems to have genuine respect for Whitebeard despite their shaky past together in the Rocks Pirates' crews and as rivals as Emperors. Whitebeard might have been Xebec's favorite subordinate too due to his strength and honnest/honorable attitude.
I guess that she has a plan to double-cross Kaido later, and she may possibly tell Perospero about it to make sure he doesn't act out of line, and Kaido surely intends to betray her too later. Perospero follows his mother's orders though I wouldn't be surprised if he instead decides to use a more subtle approach to try breaking the alliance between his mother and Kaido.
Kaido shows that he is able of using lightning techniques which isn't too surprising since eastern dragons are supposed to control weather and that OP Pirate Warriors 4 teased about him having that power, he may also use ice techniques later if Pirate Warriors 4 is to be believed again, though for now the Scabbards continue to be able of fighting and hurting him by imitating Oden's technique (though I still think it's rather cheap due to the abyss in power and skills between Oden and his scabbards, especially those who didn't get to train for 20 years). However the king of beasts is still far from defeated and once the scabbards have finally ended shining the counter-attack is going to be brutal for them.