Yes and no. The great part of Kathleen's pyscho-acceptable (that is, she is "our" psychopath) is that she can provide reasonable and valid arguments, while at the same time she can take a loss without making a fuss.
Removing August as a partner in favour of Hana means a couple of things, some of them are bad for the club: August is the Fixer, and while he resorts to illegal and violent means more often than not, he's quite correct in that an imperfect (as in violent, here) and fast solution is usually better than a perfect, yet late one (kinda military motto, btw). August, however, is not going to stop protecting the club, because it's Hana's "future", so Hana having August's part is perfect for Kathleen, because she can "leak" what she considers to August instead of having him there with a direct eye in the club.
In that regard, Kathleen is very unlikely to buy Hana's part (regardless of the issue of having the money!), but her reasoning would be "I'll keep her as long as possible", meaning "corrupt" Hana... which incidentally would be in line with August's wishes for Hana to "inherit" the whole of the family business.
But if needed, Kathleen may look for other investors that would buy Hana's part too. Ones she can control somehow. Or maybe by that time it's irrelevant since she is too old for keeping the pace.
As for the "grooming the next generation", the small problem here would be that Dr. Chuck will retire when he's dead (or with too many health problems to partake in certain excitements, and even so he looks to me like the one that will keep meddling until he dies or has a stroke), and that his "heir" would be Edwin (who seems to be more capable and determined than Ian, something coherent with having to claw his opportunities from fate, unlike "silver spoon" Ian who is so contrarian he doesn't even want to study photography... at least unless he discovers that, after bribing Edwin, his mother tried to blackmail Vicky).
TLDR, I think both Kat and Chuck don't really wanna leave, but making it look like they may spices things up, which is the sole purpose of the club.