But one plays a game. Being passive is not a game. I think this character would get a lot of grief from other Tytali. So much that he may become the center point of many games.
I'm still interested in the first point though. Would this character foster his children off to other Tytali?
Another interesting twist...after placing two of his children into other Houses, he is attempting to have his own children accepted into House Tytalus? Nominally, the master does set the gauntlet, but House Tytalus does have the tradition of the Eristic moot and using that as a means of adjusting the apprentice into the House, gradually giving the idea that the apprentice must challenge his own master in an Eristic moot. This suggests a gathering of other Tytalus, but why would they accept Kaltheus's apprentices?
Good food for thought guys - given his dark secret and clearly bad experiences with his own house that "scared him straight" he may have gone and joined House Jerbiton. It fits given the direction I want to take the character.
You OK with one of the Bonisagus later turning around and selling his apprentice to the Tytalus who inducted Kaltheus into the Titanoi? It was an offer he couldn't refuse... 
Just as a background note, you'd have to work hard to get a Jerbiton to sponsor you into the House. While Kaltheus does have Gentle Gift, and two Gentle Gifted children/apprentices, any request from a Tytatlus does have the House's legacy for deceit to overcome. 
This is kind of where I was leading to. If he is disillusioned with Tytalus then I would guess he would leave as soon as he learns his first child is Gifted so you might want to build it into his growth.
One can always join House Tytalus, but you can never leave House Tytalus. Members of House Tytalus who go to another House retain their membership in House Tytalus. No one cares, at least from an organizational point of view.
But I can see joining House Jerbiton, especially if his children have virtues that align with the House. Free Expression is a good example of a virtue that a Jerbiton apprentice character would have at character inception, and after 10 seasons it becomes the free House virtue and another appropriate virtue can be selected for the virtue point. This is something a bit different than the traditional apprentice process, but Jerbiton apprentices, more than others, are selected because of their virtues, and not strictly for their intellect. Interestingly House Tytalus probably doesn't care about an apprentice's intellect quite as much as other Houses, too.
I kind of figured that the Titanoi had a mysterious disappearance - just one part of the Dark Secret.
I'm not going to assume that Kaltheus made an immediate transfer to house Jerbiton and that it took over a decade of travel & correspondence to find a sponsor to house Jerbiton.
So I'm struggling with this history being something that describes a Dark Secret. There doesn't seem to be anything here that would destroy his standing in Hermetic circles? This seems more analogous to Tormenting Master.
I thought that murder (master, other titanoi) and diabolism were the obvious choices. 
Sure, but are you doing that, or am I?
And depending on who you murder, magi may not care.
Why murder other Titanoi?
Kaltheus was young, naive and didn't realize all the talk of getting power from spirits was code for dealing with demons. It didn't occur to him until after a summoning ritual in which he was part of - which got botched. The demon escaped and was not subdued in time leaving the other Titanoi in disarray. (Maybe two others). Having at the time, no formal knowledge of the code, Kaltheus figured his best way of escaping the situation was to kill the other Titanoi and have their bodies buried in a church graveyard. - With his mentem spells he could have "convinced" a priest to do his bidding. It was likely conversations with the priest about the nature of the bodies that it really got to him about what he'd done and he decided to try and redeem himself.
Luckily so far for Kaltheus, the other Titanoi were not well liked and prone to long disappearances.
Ok, I can work with that.
Just for your edification (as the player), not all Titanoi are actually diabolists. Kaltheus can, and probably, does think of that all of them are.
Edit: Oh, and Kaltheus is a Jerbiton, right? Or consider House Criamon and one of their paths as a method for seeking atonement...
Hadn't thought of Criamon actually - worth some thought. I was thinking Jerbiton - I'll get back to you.
It was a flash of inspiration I had about the character, and the House welcomes anyone. Jerbiton is a bit more restrictive about who comes in, although Kaltheus has enough virtues to join...
Yeah, it's a good point.
Also re: Titanoi - yes I'm personally very much aware that they're not all Diabolists. Kaltheus thought that they weren't Diabolists either and is no longer sure what to think of them other than stay far far away.
Do you want to know more about the situation than your character knows?
Sure.
I'll start updating his character sheet soon - I've been wanting to figure out the direction first. My thought is that Kaltheus will join house Jerbiton. The write up for Criamon is the first rpg supplement that makes my eyes glaze over followed by an urge to throw my book against the wall. While it could very well work for the character, for me as a player, House Criamon is just too weird.
Now - just to check, for inventing spells, I just trade in 1xp = 1 level rather than calculating lab totals?
With the Pious flaw, he fits into the Path of Walking backwards quite nicely. While it is based on a Sufi practice I can easily see it being any divine following.
Regarding spells, yes, but you need to have the lab total sufficient to getting the spell as per RAW.
I understand regarding Criamon.