Knowing Oda, he didn't give Kaido a son, just to have another strong man on the Beast Pirates side.
Powerful, maybe, but Oda is going to explore the father-son relationship & dynamic between the two, I can already see a story as old as time:
'Parent gets mad because kid is up in his room not showing his face (shut in?) when ther're guest over'.
"My Son, is he going to show up at the very least, this is a banquet!"
So I think we can at least surmise that their relationship is a bit "strained". Way Kaido is, he may have harshly parented his son, in effort to make son more like him, when he's not, which could have strained their bond; Kaido's an alcoholic with a range of emotions in that state so that could add more strain.
But I expect something a bit different cuz we've already seen this type of father-son relationship in Judge and Sanji.