One of The Phantom's primary plot points in any incarnation is that the Walker clan maintains the illusion that The Phantom is the same person, by passing the mantle on from father to son. It can be expected that becoming not just a vigilante but a jungle legend is something that requires more than a little "on the job" hands-on training, so naturally father and son will be out in the jungle together quite a bit. But what kind of jungle grass was the elder smoking to decide to make Junior an identical Phantom costume to wear (sans the maroon color) while out there with him late in his training??? And totally unforgivable was Junior actually telling the "hostage" in Issue 7 that he is going to be the next Phantom. Even if they didn't realize she was in on it all along, generally The Phantom keeps the illusion up with all but his closest allies as well as his enemies.
The Dynamite series had an interesting way to deal with this. The Phantom-to-be had a red costume, with yellow-striped outside-undies. It was a nice nod to the versions of the Phantom comics published in countries where he wears just that, though arguably it isn't any better, here. It's still designed the exact same, and the Phantom-to-be in question actually says to the woman he's rescuing that the man in purple she asked about was the Phantom, and he was the next Phantom.
It's a requirement that each Phantom marries and has children, to carry on the legacy. So why was Kit's father so disapproving of his plan to marry? Unless of course Kit had already decided to forsake the Phantom legacy anyway, and his father knew it...
Perhaps he just didn't approve of Kit's choice of spouse?
Perhaps he was fine with the choice of spouse, but angry that Kit chose not to become the Phantom. Maybe he secretly blamed the woman and the marriage for that choice.